text:
ICT4 Elderly/Online Payments

Contents of the module
 * Online payment transactions with tools available (PayPal, etc.);
 * Online payment terminology;
 * Buy and sell options;
 * Consumer rights and return policies;
 * Safety tips (passwords, secure websites, scams).

Learning objectives
 * To choose the most suitable online payment provider;
 * To understand different kinds of online payments (Paypal, credit card, debit card, …);
 * To be aware of the importance of safety protocols when using online payment methods;
 * To be aware of consumer rights and different types of return policies;
 * To enable the learner to safely make purchases on the internet;
 * To raise awareness of e commerce and trading on the internet.

Learning outcomes
 * Participants are able to make online payments and are familiar with four main steps: (1) registration, (2) making an e-payment, (3) verifying payment and (4) acknowledging e-payment receipt;
 * Participants are able to check Payment status;
 * Participants are using only strong and unique passwords and are making payments only through secure websites;
 * Participants are able to adjust their browser safety settings and are able to use the default firewall security protection on their computers;
 * Participants are able to actively participate in different online market sites - buying and selling different items.

Learning scenario
 * A discussion with the lecturer and participants about their previous experiences with online payment, shopping and online payment providers;
 * A presentation on online payments system;
 * Interactive presentations of online payments and market sites;
 * Exercise on using an online payment provider and creating an account, afterwards using online shopping page (e.g., E-bay) to simulate online payment of one item of their choice;
 * A group discussion about the advantages and disadvantages of using online payments;
 * Videos.

Evaluation
 * Evaluation will be held through a special assignment: every participant will have to explore E-bay and to simulate online payment of one item of their choice.

Following this module learners will:
 * Participants are able to make online payments and are familiar with four main steps: (1) registration, (2) making an e-payment, (3) verifying payment and (4) acknowledging e-payment receipt;
 * Participants are able to check Payment status;
 * Participants are using only strong and unique passwords and are making payments only through secure websites;
 * Participants are able to adjust their browser safety settings and are able to use the default firewall security protection on their computers;
 * Participants are able to actively participate in different online market sites - buying and selling different items.

Online Payments Systems
What does an online payments site do? Online payment sites are used to transfer money from a customer’s credit or debit card to a merchant or suppliers bank account

How is an online payment made?
A – To buy something the Customer enters their credit or debit card details at the Online Merchant checkout site

B – The Online Merchant transfers the payment card details to their selected Payment Gateway

Payment Gateway companies include: PayPal, WorldPay, Stripe, VeriSign, Stripe. Dwolla, Google Wallet and Amazon Pay.

C – The Payment Gateway connects the merchant to the Card Payment Network

Card Payment Network companies include: MasterCard and Visa

D – The card payment network is the glue between the various Payment Gateways and the Card Issuing Bank, and makes the request for payment from the customers bank account at the Card Issuing Bank

Card Issuing Bank is the bank that gave (issued) the physical debit or credit card to the customer

E – The Card Issuing Bank approves, or rejects, the payment request

The Card Issuing Bank passes back the payment approval / rejection details back through the chain to the Card Payment Network, Payment Gateway, Online Merchant and finally to the Customer

F/G/H – If the payment is approved by the Issuing Bank, it transfers the customers money from their bank account to the merchants bank account – this is called Settlement.

What credit/debit card information does the Customer need to supply?
It depends on the online merchants website! The following 5 elements can be requested:

Cardholder Name – as written on the front of the card

16 digit card number – also known as the Primary Account Number (PAN) – this is linked to the customers bank account (Mandatory)

Card Expiry Date – as written on the front of the card (Mandatory)

Card Verification Value (CVV2) – a 3 digit number on the back of the card

The idea of the CVV2 number is for added security, the idea being only you know and see  this information because you’re in possession of the card.

Cardholder Address – this is not written on the card, but is often used to verify the customer.

Keywords
Online payment, Credit card, Debit card, Payment network, PayPal, WorldPay, Stripe, VeriSign, Stripe, Dwolla, Google Wallet, Amazon Pay.

Material required

 * Personal computer (Smartphone or tablet connected to the Internet)
 * Internet connection
 * Beamer
 * Paper and pens
 * Flipchart
 * Speakers

Session structure
The purpose of the session will be:

 * to provide an introduction to to make online payments
 * to facilitate four main steps: (1) registration, (2) making an e-payment, (3) verifying payment and (4) acknowledging e-payment receipt
 * to discover safety settings and are able to use the default firewall security protection on their computers
 * to motivate to actively participate in different online market sites - buying and selling different items

Introduction
For the introduction, the lecturer will begin by asking participants about their previous experiences with online payment, online shopping, and online payment providers. With this approach, the lecturer and participants will develop an inclusive learning field for the lecture which follows

Online payement
The content of the lecture will be based on the concept of online payment and various methods of online payment. In order to make online payment, we first need to select an online payment provider, a connection between a bank and an online payment provider, and finally a smart device through which we will make payments. The next step in the lecture, however, is the payment process. Participants will be shown basic payment steps, wire transfer, payment receipt, account balance. The last step, which is also very important, is to ensure security when setting up online payments.

Online payement methods
Everyone opens his/her laptop

Task - Each participant will need to find the most appropriate online payment provider and create an account. Then every participant will have to explore E-bay and use online payment for buying and selling one item of their choice after the finished module.

Group discussion
Finally, there will be a group discussion about the benefits of paying again and using the most appropriate online payment provider. During the debate, participants will be able to share views, concerns, experiences and other information relevant to setting up online payment accounts.

Homework
Watch video and make comments

Understanding Online Payments

Debriefing
To wrap up the session, the trainer will facilitate a debriefing moment where participants are encouraged to express their questions, doubts, ideas and feelings toward the topics discussed.

Evaluation
Participants will answer a small questionnaire to evaluate the form and the content of the session.

Overall duration of the session
1 hour and 20 min

title: ICT4 Elderly/Online Payments


text:
User:LBird BASc/sandbox/ATK/Seminar6/Power/Power in Arts

Importance of Connections
There is a pattern that artists become famous not for their originality and creativity, but the network they have. People who have parents who are artists or people who grew up surrounded by artists are more likely to get their works demonstrated in galleries, get wider recognition than the ones who have original and outstanding works, but they do not have a wide network. Paul Ingram and Mitali Banerjee made a study on what made artists famous. They used various sources as biographies, books, letters, etc. to find artists' social networks. To analyze originality of artworks they used machine learning. The results showed that the best known creators were in the same social circle. Moreover, big indicator of one becoming famous was having connections in other countries. There was not big link between the originality of one's art and person's fame. . Which makes successful in art field depend on the background people have, but not their skills and effort they make.

Rich People in Arts Field
It is not a secret that a lot of people are afraid to choose artist profession because of the financial reasons. Looking through the history it is obvious that often artists lived in poverty. Now it is easier to become famous using social media, also, there are more galleries, art fields to work in, nevertheless, finding a job in arts fields is more favorable for wealthy people. The situation is worst for youngsters who are in the begging of the path to becoming artists. As internships in arts field are usually unpaid. Sutton Trust's survey shows that 86% of internships are unpaid. This means, that young people who grew up in richer families are more likely to become artists, as they do not have to worry of making ends meet and can devote all their time to develop needed skills, grow their network and create. Meanwhile, poorer people have to search for additional job to support themselves, thus, even with a bigger talent they may take more time to reach success or they even might have to choose a different career.

Women Artists
Half of the visual artists are women according to the National Museum of Women in the Arts, but for instance in London almost four fifths of galleries display more men works than women. Women were unrepresented in arts field for a very long time. It was a social norm that women have to take care of all house chores, children and there is not much time left afterwards. Also, they could not get into art schools, this means they got less opportunities to develop their skills and to become known by other. Additionally to all these obstacles in general they were considered less worthy artists than men. For instance, nowadays a very famous Mexican painter Frida Kahlo used to be in the shadow of her husband. In 1938 when she had her first exhibition, Vogue preferred naming her as “Madame Diego Rivera.” It demonstrates how important a man role was in the art world.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
LMIs in Control/Stability of Lure's Systems

The System

\begin{align} \dot x(t)&=Ax(t)+B_pp(t)+B_ww(t),\\ z(t)&=C_zx(t)\\ p_i(t)&=\phi_i(q_i(t)), i=1,\dots, n_p\\ q&=C_qx,\\ 0 &\leq \sigma \phi_i(\sigma) \leq \sigma^2 \ \forall \sigma \in \mathbb{R} \end{align}$$

The Data
The matrices $$ A,B_p,B_w,C_q,C_z $$.

The LMI: The Lure's System's Stability
The following feasibility problem should be solved as sufficient condition for the stability of the above Lur'e system.

\begin{align} \text{Find} \; &P>0,\Lambda=diag(\lambda_1,\dots,\lambda_{n_p})\succeq 0, T=diag(\tau_1,\dots,\tau_{n_p}) \succeq 0:\\ &\begin{bmatrix} A^\top P+PA & PB_p+A^\top C^\top_q \Lambda +C^\top_q T \\ B^\top_p P + \Lambda C_qA+TC_q & \Lambda C_q B_p+B^\top_p C^\top_q \Lambda-2T \end{bmatrix} \prec 0\\ \end{align}$$

Implementation
https://codeocean.com/capsule/0232754/tree

Conclusion
If the feasibility problem with LMI constraints has solution, then the Lure's system is stable.

Remark
The LMI is only a sufficient condition for the existence of a Lur’e Lyapunov function that proves stability of Lur'e system. It is also necessary when there is only one nonlinearity, i.e., when $$ n_p = 1 $$.


text: Wikibooks:Collections/LMIs in Control/ LMI for Continuous Time and Discrete-Time Asymptotic Stability


text:
User:LBird BASc/sandbox/ATK/Seminar6/Evidence/Evidence in Political Science

Evidence in Political Science
Evidence in political science plays a key role in providing political scientists with accurate information on the issues which they are investigating, thus helping them land safe conclusions about these issues. Evidence can resolve the ambiguity, check the correctness of the existing theories, and shed light on future studies. Both qualitative tools and quantitative tools are applied by political scientists to acquire evidence, and the tools they use can be somewhat different from other subjects due to the nature of political science. With evidence obtained from all these methods, scientists can move on to make predictions about specific trends in politics, and offer people with information that are needed in political debates, and make contributions to the policy-making process.

Qualitative Evidence
In political science, Qualitative research can be defined as a process of inquiry that builds a complex and holistic picture of a particular phenomenon of interest by using a natural setting. There are several ways to gather qualitative evidence: ethnographic studies, phenomenological studies, case studies, focus groups, and intense interviews. One of the limitations of qualitative evidence is that while looking for this sort of evidence scientists tend to focus on a particular case and fail to take the whole picture into consideration. For example, in intense interviews, despite the fact that political scientist will interview a large number of people who are related to the research and try to make sure the interviewees come from diverse backgrounds and socioeconomic conditions, there still exist the possibility that they neglect some groups of people who should be involved in the study, which leads to a partial conclusion.

Quantitative Evidence
Quantitative research can be defined as a process of inquiry examining an identified problem that is based on testing a theory measured by numbers and analyzed with statistical techniques. Therefore, quantitative evidence is mostly data obtained by the political scientists. There are several ways to get useful quantitative evidence, including experiments, quasi experiments, content analysis, and surveys. Despite that quantitative evidence is usually a convincing source, some scientists also point out that this sort of evidence has limitations. For example, some argue that quantitative evidence is partial since scientists ignore the unique cultural roots and other aspects of the marginalized groups.


text:
User:LBird BASc/sandbox/ATK/Seminar6/Power/Power in History

Introduction
Bo Yang, a Chinese poet, historian and essayist based in Taiwan, published An Outline of Chinese History in 2002. This book was the first Chinese chronology expressing time in a Western format. Different from previous history work which expressed time in terms of each emperor's reign, Bo Yang used centuries and BCE/CE. As a result, this work better reflects how the historical changes impacted the life of ordinary Chinese people than other chronologies. Instead of entirely focusing on the contributions made by emperors, officials or army generals, this book covers lots of stories of people from lower classes whose names are unknown due to the lack of records and pays attention to their social conditions.

Power in History
Power plays a great role in history study. Those who were in higher positions tend to appear more often in all kinds of historical works, and this can in turn leave a false impression on readers that these people were the only ones who changed the course of the human history and make them fail to realize how the ordinary people contributed to the historical movements. Apart from power in terms of social classes, power related to gender is also a major element in shaping the historical narrative. Women were usually written out of history. Women aren’t allowed to be characters in history, and they have to be stereotypes.

Methods to deal with power in history
We should work hard to fill the gaps which are caused by power. Bo Yang has already offered us a good example in doing this. First, historians could consider change the way they write history works, which means instead of following the old traditions passed down by the former historians they could make an attempt to create new ways of narrative that include rather than exclude people from usually ignored groups. Second, historians should try to uncover more historic evidence related with lower-class people and women, and fully present it in the history work.


text:
Mathematical Methods of Physics/Fourier's theorem

Skip to main content Toggle navigation Home University of Jos - Nigeria Search Keywords Search NAVIGATION

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Library Resources Department Of Physics

DEPARTMENT OF PHYSICS The Department of Physics is one of the foundation departments of the Faculty of Natural Sciences. From September, 1973, it prepared students for the direct entry to the University of Ibadan of which the present University was a Campus. By 1979 the Department produced its first batch of graduates in Physics and in 1983 the first batch of Postgraduate students passed out.

LOCATION OF PHYSICAL FACILITIES

The Department has 4 blocks of laboratories and an Atmospheric Physics observatory at the Bauchi Road Campus. The prefabricated structures were originally equipped for the 100 and 200 level practical work. One of them is on loan to the Department of Remedial Studies. The first floor of the storey building by the side of A1 accommodates 100 and 200 level laboratories, staff offices, toilets, staff common room and a lecture room for about 50 students (Room 201) reserved for 300 level lectures mainly. The Physics Laboratory III is equipped for 300 and 400 level practical work. The Postgraduate Common Room is located there. A Seminar room capable of seating 40 students in that block is reserved for 400 level lectures and Department seminars. In addition to the offices attached to the Laboratories, the following offices are available to the Department:

Natural Sciences Admin. Complex – Rooms 30, 31, 32 and Rooms 50, 51, 52, 54, 55, 56, 57 in the former Social Sciences Block.

The Physics store is located opposite the University Primary School, it houses spare laboratory equipment in addition to those equipment awaiting repairs.

Philosophy, Goals and Objectives Admission Requirements Relevance of Programme Grading Methods Award of Degree Programme content Presented below are the courses offered in the Department. The availability of some of the courses listed under electives depends on the staffing situation in the Department. The courses are codified with the letters PHY followed by a three-digit code. The first digit in the course code represents the level of study in a four-year degree programme i.e 1,2,3 & 4 for the 1st, 2nd, 3rd & 4th years of study respectively.

100 Level 200 Level 300 Level 400 Level COURSE

CODE

CORE COURSES

CREDIT

UNIT

SEM.

PHY 401

QUANTUM MECHANICS I   PRE: PHY305

3

1

PHY 402

QUANTUM MECHANICS II   PRE: PHY401

3

2

PHY 403

MATHEMATICAL METHODS OF PHYSICS I  PRE:MTH 201 & 204

3

1

PHY 404

MATHEMATICAL METHODS OF PHYSICS II PRE: MTH304

3

2

PHY 407

COMPUTATIONAL PHYSICS   PRE: MTH201

3

1

PHY 413

ANALYTICAL MECHANICS II PRE: PHY 301

3

1

PHY 431

OPTICS II   PRE: PHY 331

3

1

PHY 443

ELECTROMAGNETIC WAVES & OPTICS PRE: PHY 303

3

1

PHY 455

SUPERVISED INDEPENDENT RESEARCH (PROJECT WORK) (PRE:No lower courses of more than 12 units)

6

1&2

PHY 491

RESEARCH METHOD

2

1

PHY 497/498

EXPERIMENTAL PHYSICS VI & VII  PRE: PHY 307/308

2

1 & 2

FOR D.E CANDIDATES

GST 101

USE OF ENGLISH

4

1,2

GST 102

PHILOSOPHY AND LOGIC

2

2

ELECTIVE COURSES

PHY 411

NUCLEAR AND PARTICLE PHYSICS I

2

1

PHY 412

NUCLEAR AND PARTICLE PHYSICS II    PRE: PHY411

2

2

PHY 423

SOLID STATE PHYSICS II  PRE: PHY 314

2

1

PHY 435

ACOUSTICS II   PRE: PHY 335

2

1

PHY 445

RELATIVITY & ELECTROMAGNETISM    PRE: PHY 303

2

1

PHY 461

DIGITAL ELECTRONICS     PRE: PHY 361

2

1

PHY 465

INSTRUMENTATION & MEASUREMENT   PRE: PHY 361

2

2

PHY 466

COMMUNICATION & INFORMATION THEORY   PRE: PHY 361

2

2

PHY 484

ATMOSPHERIC PHYSICS II    PRE: PHY 381

2

2

PHY 434

BIOPHYSICS II   PRE: PHY 334

2

2

PHY 432

APPLIED OPTICS    PRE: PHY 331

2

1

PHY 433

PHYSIOLOGICAL OPTICS

2

1

PHY 424

ATOMIC & MOLECULAR SPECTROSCOPY

2

1

PHY 486

INTRODUCTION TO GEOPHYSICS II  PRE: PHY 383

2

2

SERVICE COURSES TO FACULTIES OF ENGINEERING, MEDICAL, VETERINARY & PHARMACEUTICAL SCIENCES Course Description DEPARTMENTS

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text:
Lentis/Featuritis

Introduction
Featuritis, or, is the expansion or addition of features to a product that go well beyond the project's original scope or intent. Although this phenomenon of product development can occur in any field, the continuous integration and continuous delivery (CI/CD) practices common to software development often result in featuritis. These practices make the channels that develop and deliver content to the user extremely efficient. As the development of updates becomes faster, the utility of the content within them can become questionable to the end user. This chapter studies the causes and effects of featuritis and offers potential solutions to eliminate it.

Disconnection from User Base
The effectiveness of new features is derived from their utility to the user base. If a developer does not take the time to properly reach out to their users regarding product usage and, then any features that are added run the risk of being useless to the end user. Although developers can make guesses on what the end user will find useful, taking the time to collect user feedback on the performance of existing features and what new features they would like to see greatly decreases the likelihood of a product suffering from featuritis.

Desire to Increase Market Space
As the number of functionalities of a product increases, the potential to appeal to a larger audience increases. If a company wishes to increase the target audience for a product, they may add features that specifically appeal to that market. Although this increases the number of potential customers, it makes the product lose focus on its original user base. Long time users may feel that the product is becoming less useful to them as the features they used in the past become outdated in the efforts to create new features.

This can also be applied in the attempt to maintain users. A company can prevent their current customers from switching to a competitor's product that has different features by including them within their own product. This can be done similarly in order to regain users lost to a competitor. This is dangerous because the desires of the user base of the competitor's product can be slightly different, leading to features that are not particularly useful to those that continue to use the product.

Demand Creation
Features can be added to products in the hopes of creating demand. If the features that are added to new products are deemed useful, or at least interesting enough, by the users, they will be more inclined to buy the newer product regardless of the usability of their current product. As a result, companies can increase the overall lifetime value of their customers by persuading them to buy newer products before they need to through the addition of seemingly useful features. In reality, these features may be nothing more than smart marketing tactics that leave the user with a product that is nearly identical to the one that they already had.

Consumerism
In the current economy, consumers have become greatly accustomed to having new products being developed in a very short period of time. Regardless of the market they are shopping in, customers will be looking to see new products as soon as they can. As a result, they will put pressure on developers to create new functionalities or match the functionalities of different products. While this can help companies easily market and sell new versions of their products, it also puts a great deal of stress on coming up with new features. If developers cannot create new and useful features at the same speed that consumers are demanding new products, they run the risk of having to add meaningless, but easy to implement, changes that can result in featuritis.

Silent Majority / Vocal Minority
With the rise of social media, many software products suffer when developers cater to the vocal minority and ignore the. The silent majority are users who are satisfied with the product as a whole and do not have any incentive to leave their opinion. The unsatisfied vocal minority will most often request new features. From the developer's point of view, it seems like these features are being widely desired by the entire user base, but in reality, it is only a small subgroup of users. As a result, the features that appeal to the silent majority of users may be ignored in order to focus on those that the vocal minority demands.

Short-term Profitability
Consumers will opt for products with more features even if they are aware that the product could be more difficult to use. Companies increase the functionality of their products in order to enhance or differentiate them. Carpenter et. al. (1994) found that brands can differentiate themselves by including meaningless features to their products. However, if core functionality is sacrificed in this process, post-purchase consumer dissatisfaction and lower overall lifetime value results, as user preferences shift from functionality to usability after purchase.

Time Loss
Developer time is not unlimited. As developers spend more time adding features, they focus less on the core functionalities of the product. This can result in or in the loss of core functions. Even more time can be lost if core functionality is affected, as the developer may be forced to halt production until they resolve the issue.

Smartphones have become ubiquitous in recent years, and manufacturers must quickly and effectively develop their products to succeed in the market. Samsung developed a smartphone that could fold in half during 2018. In April 2019, Samsung cancelled the release of the new smartphone after several broke during media testing. The phones were released for sale in September. Because the feature was underdeveloped, the phones became unusable and several months of time were required to solve the issues related to the new features.

Decreased Maintainability
Regardless of the functionality of a code base, maintenance becomes more costly and time consuming as features are added to a product due to increased complexity. It is estimated that more than 50% of software life cycle costs are due to maintenance. Products with an excessive amount of features may suffer from more bugs and issues that require maintenance than those that have few core functions. As the amount of required maintenance increases, developers must devote more resources to maintenance or accept worse performance from the product.

Decreased Usability
As developers add features to a product, the user interface can become crowded and difficult to use. Core functionality can be lost or hindered by secondary functions as locations of features change or become more difficult to navigate. As consumers value usability after purchasing a product, consumers dissatisfaction may result.

The BMW system is the user interface for the computer system that controls the secondary functions of BMW automobiles. It debuted on BMW 7 series automobiles in 2002. The original system received harsh criticism from the public due to its complexity and poor usability. The system employed a single rotating knob on the center console that was used to navigate through the control panel. While the system did eliminate numerous buttons and knobs, users found it difficult to navigate and confusing. One reviewer noted that six steps were required to change the radio station. The system has since been heavily remodeled to provide a better user experience. Current iterations have a smaller knob that controls fewer features, a touchscreen that resembles a tablet, and the ability to recognize voice commands as well as hand gestures for controlling features.

Smart home technology has become commonplace with the proliferation of WiFi-enabled devices. The technology includes devices that can control functions in homes such as lighting, doors, heating and air conditioning, and control of appliances from a mobile device. While the vision of controlling all home appliances with the push of a button has existed since the mid-20th century, the technology has not been widely accepted due to functionality problems. Users complain of difficulties in integration of devices, a steep learning curve, and undesired functions. Many homeowners opt for traditional systems like light switches, standard appliances, and mechanically-locking doors because they perform their intended function reliably and require no learning curve.

Software Bloat
occurs when a product increases in size, memory usage, minimum hardware requirements, etc. without having any measurable difference between previous versions. In extreme cases, newer versions can have performance issues that make it slower than its predecessor. Users may become frustrated with products experiencing software bloat due to the slower performance speeds. Additionally, many of the features being added that contribute to these slower speeds are not useful to them (or a majority of the other users).

Critically Analyze New Features
Project managers can often times get carried away with adding features since fixing bugs in their system is not as flashy and rewarding for the company. This type of mentality accelerates feauritis. Therefore, when considering if a new feature should be implemented there are two important things to consider: how many people will use it, and how often will they use it. For example, if a new feature will be used by all of the users, all of the time, then that is a great feature and should be implemented. On the other hand, if a new feature will be used by few of the users, all or most of the time then that might not be the best use of time. There could possibly be some current features that need improvement or some outstanding bugs that need squashing.

Bug Fixing
As previously stated, implementing new features should take a back seat to bug fixing under certain circumstances. Therefore, a fix-bugs-first methodology should be adopted when trying to reduce feauritis. This methodology focuses on fixing all the bugs in the current feature set first instead of pushing new features with every release of the product. Thereby users are not overloaded with features and instead feel like their feedback is valued, appreciated, and implemented. This methodology will make the core features strong.

Pruning
The idea is to focus on cutting out unnecessary features in the system while enhancing the core ones. In a metaphor, focus on creating a strong root and trunk before creating several branches. Deciding which are core features entails listening to the user base and analyzing their use cases. Then critically analyze features in the same manner as aforementioned to find the core features of the system. After pruning, both of the aforementioned solutions should be implemented to stop or reduce feauritis in the system. Pruning reveals which highly utilized core features are being neglected, and should be improved, while removing underutilized components. The main takeaway is on the main components of the product and perfecting them.

Modularization
In a similar manner to pruning, modularization is about splitting the system into its main components and then having additional add-ons. This way, users can add to the software or product as they need or want instead of being overloaded all at once. The extra features that were removed during pruning could turn into additional modules. The user then has a much more customized experience and can use add-ons as needed or as expertise increases. Therefore, the complexity that the user builds does not appear to be feauritis because the user is comfortable with each addition to the system. An example of this in Computer Science is the idea of frameworks. For example, React Native is an open source framework created by Facebook for building native mobile apps. Facebook focuses on supporting and maintaining the framework while developers around the world create libraries, or add-ons, that can be imported and used in the framework. Therefore, at the core of every React Native app it is using the same framework but the components, add-ons, or features built on top of it are all completely different.

Configurable User Modes
Similar to modularization except add-ons are group together and preset by the system. There are certain software or technologies that need to have a plethora of features in order to support the vast, almost endless, use cases. In these scenarios, developers can implement user modes that show and hide different features. This allows the user to change between modes based on their experience with the system. Therefore, a new user can start at a beginner mode and switch into other modes as they get more comfortable and gain expertise. This will reduce the feature overload of a first-time user being put essentially in expert mode right out of the box.

is a computer-aided design software package that allows users to configure the interface to their needs. Instead of displaying the twenty available ribbons at once, the default screen shows the seven most essential ribbons and an "Add-ins" ribbon that contains the remaining specialty ribbons. There are numerous hidden toolbars that can be accessed by clicking in the appropriate location. The side windows can be minimized and re-positioned. These functions allow the user to tailor the interface to their work and provide all desired features when required, and illustrate how configurable user modes can enhance the usability of feature heavy software.

Conclusion
Featuritis develops from the interaction of the competing agendas of the consumers, product developers, and marketing teams. In accordance with, the most complex solution is often not the best solution. As demonstrated by the case of the Samsung foldable smartphone, too much emphasis on new features will cost the developer serious amounts of time and money if core functionality is not maintained. Product features may be revolutionary, but consumers will only invest if the product is as reliable as previous versions and easy to use. Further work on featuritis may include the further study of the long term effects additional product features on profitability, how user feedback affects developer decision-making and practice, and the effectiveness of agile product development.

title: Lentis/Featuritis


text:
User talk:86.63.9.30

stop rolling back my stuff

--Pi zero (discuss • contribs) 15:41, 13 November 2019 (UTC)

title: User talk:86.63.9.30


text:
User:Ɨøɨœɵɜɨ/sandbox

superman'

title: User:Ɨøɨœɵɜɨ/sandbox


text:
User:CongruentSquare/sandbox

The Student's Manual to 'The Art Of Electronics' 3rd edition
A work-in-progress guide and solution set to Paul Horowitz and Winfield Hill venerable book 'The Art Of Electronics' 3rd edition(ISBN-13: 978-0521809269). "Exercise 1.1 You have a 5K resistor and a 10k resistor. What is their combined resistance (a) in series and (b) in parallel""Exercise 1.2 If you place a 1 ohm resistor across a 12 volt car battery, how much power will it dissipate?""Exercise 1.3 Prove the formulas for series and parallel resistors."

title: User:CongruentSquare/sandbox


text:
LMIs in Control/Stability Analysis

 * /Continuous Time/
 * /Discrete Time/
 * /Lure's Systems/
 * /Stability of Systems with Integral Quadratic Constraints/
 * /Sector Conditions/
 * /Kharitonov-Bernstein-Haddad/

title: LMIs in Control/Stability Analysis


text:
LMIs in Control/Stability Analysis/Stabilizability LMI

Stabilizability LMI

Stabilizability is a essentially a weaker version of the controllability condition. A system is stabilizable if all unstable modes of the system are controllable. This implies that if the system is controllable, it will also be stabilizable. The LMI condition for stabilizability of pair $$(A,B)$$ is shown below.

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t),\\ x(0)&=x_0, \end{align}$$ where $$x(t)\in \R^n$$, $$u(t)\in \R^m$$, at any $$t\in \R$$.

The Data
The matrices necessary for this LMI are $$A$$ and $$B$$. There is no restriction on the stability of A.

The LMI: Stabilizability LMI
$$(A,B)$$ is stabilizable if and only if there exists $$X>0$$ such that
 * $$AX+XA^T-BB^T<0$$,

where the stabilizing controller is given by
 * $$u(t)=-\frac{1}{2} B^TX^{-1}x(t)$$.

Conclusion:
If we are able to find $$X>0$$ such that the above LMI holds it means the matrix pair $$(A,B)$$ is stabilizable. In words, a system pair $$(A,B)$$ is stabilizable if for any initial state $$x(0)=x_0$$ an appropriate input $$u(t)$$ can be found so that the state $$x(t)$$ asymptotically approaches the origin. Stabilizability is a weaker condition than controllability in that we only need to approach $$x(t)=0$$ as $$t\rightarrow \infty$$ whereas controllability requires that the state must reach the origin in a finite time.

Implementation
This implementation requires Yalmip and Sedumi.

https://github.com/eoskowro/LMI/blob/master/Stabilizability_LMI.m

Related LMIs
WIP: Will be linked once they have been created.

Controllability LMI

Hurwitz Stability LMI Schur Stability LMI

Observability LMI

Detectability LMI

Controllability Grammian LMI

Observability Grammian LMI


text:
LMIs in Control/Stability Analysis/Detectability LMI

This is a Template for Creating An LMI Page

The System

\begin{align} \dot x(t)&=Ax(t)+B_pp(t)+B_ww(t),\\ z(t)&=C_zx(t)\\ p_i(t)&=\phi_i(q_i(t)), i=1,\dots, n_p\\ q&=C_qx,\\ 0 &\leq \sigma \phi_i(\sigma) \leq \sigma^2 \ \forall \sigma \in \mathbb{R} \end{align}$$

The Data
The matrices $$ A,B_p,B_w,C_q,C_z $$.

The LMI: The Lyapunov Inequality
Title and mathematical description of the LMI formulation.

\begin{align} \text{Find} \; &P>0,\Lambda=diag(\lambda_1,\dots,\lambda_{n_p}), T=diag(\tau_1):\\ \begin{bmatrix} X\end{bmatrix}&>0\\ \begin{bmatrix} A^T X+XA\end{bmatrix}&<0 \end{align}$$

Conclusion:
Interpretation of the results of the LMI

Implementation
A link to CodeOcean or other online implementation of the LMI

Related LMIs
Links to other closely-related LMIs


text:
LMIs in Control/Stability Analysis/LMI for the Controllability Grammian

This is a Template for Creating An LMI Page

The System

\begin{align} \dot x(t)&=Ax(t)+B_pp(t)+B_ww(t),\\ z(t)&=C_zx(t)\\ p_i(t)&=\phi_i(q_i(t)), i=1,\dots, n_p\\ q&=C_qx,\\ 0 &\leq \sigma \phi_i(\sigma) \leq \sigma^2 \ \forall \sigma \in \mathbb{R} \end{align}$$

The Data
The matrices $$ A,B_p,B_w,C_q,C_z $$.

The LMI: The Lyapunov Inequality
Title and mathematical description of the LMI formulation.

\begin{align} \text{Find} \; &P>0,\Lambda=diag(\lambda_1,\dots,\lambda_{n_p}), T=diag(\tau_1):\\ \begin{bmatrix} X\end{bmatrix}&>0\\ \begin{bmatrix} A^T X+XA\end{bmatrix}&<0 \end{align}$$

Conclusion:
Interpretation of the results of the LMI

Implementation
A link to CodeOcean or other online implementation of the LMI

Related LMIs
Links to other closely-related LMIs


text:
LMIs in Control/Stability Analysis/LMI for the Observability Grammian

This is a Template for Creating An LMI Page

The System

\begin{align} \dot x(t)&=Ax(t)+B_pp(t)+B_ww(t),\\ z(t)&=C_zx(t)\\ p_i(t)&=\phi_i(q_i(t)), i=1,\dots, n_p\\ q&=C_qx,\\ 0 &\leq \sigma \phi_i(\sigma) \leq \sigma^2 \ \forall \sigma \in \mathbb{R} \end{align}$$

The Data
The matrices $$ A,B_p,B_w,C_q,C_z $$.

The LMI: The Lyapunov Inequality
Title and mathematical description of the LMI formulation.

\begin{align} \text{Find} \; &P>0,\Lambda=diag(\lambda_1,\dots,\lambda_{n_p}), T=diag(\tau_1):\\ \begin{bmatrix} X\end{bmatrix}&>0\\ \begin{bmatrix} A^T X+XA\end{bmatrix}&<0 \end{align}$$

Conclusion:
Interpretation of the results of the LMI

Implementation
A link to CodeOcean or other online implementation of the LMI

Related LMIs
Links to other closely-related LMIs


text:
User:Sophiehanton1/sandbox

Power in policing In this piece I will look at power in policing and specifically the tactic of stop and search.

The tactic of using stop and search, was first introduced in the 1981 to tackle high levels of crime in south london, specifically Brixton. Police stopped and searched hundreds 943 mainly black youths. The operation was a Major catalyst for the Brixton riots in April of 1981.

New rules on the way police can use the tactic have been introduced, for example generally they need reasonable evidence that the suspect has been involved in a crime or carrying illegal items. However, still today it remains one of the most controversial police tactics and is frequently referenced when talking about racism with the police.

A report by the 'Equality and Human Rights Commission' in 2010, concluded that police across the country disproportionately used the tactic against black and Asian people. It stated 'the pattern of entrenched disproportionate use of stop and search powers' correlates to 'evidence on racial prejudice and stereotyping'. This idea of racial prejudice as a driving force for how police chose who to stop and search is problematic. As the report explains, if police are making decisions based on prejudices and generalised beliefs, rather than objective evidence the tactic is not being used in a lawful way. The findings in this report are still relevant today, for example in 2018 black people were nine times more likely t stopped and searched than white people. Furthermore Theresa May's relaxation of regulation around the tactic this year has worsen the imbalance between racial groups.

Studies have shown that the disproportionate is in part caused by decision making based on racial bias. Stop and search is 60% linked to drugs, and David Lammy, the MP for Tottenham believes the discrimination is 'grounded in the fictitious narrative that drug use is especially prevalent among black and minority ethnic groups'. However the stereotype of drug use and increasing like-hood of criminality among particularity black men, is not backed by evidence-only 16% of stop and searches of black people involving knives resulted in arrest compared 21% for white people, in 2019.

However, in the context of knife rising 7% this year, police have backed the bias of stop and search against Black youths stating '

title: User:Sophiehanton1/sandbox


text:
User:Vasenthi/sandbox

The System
Consider a contiuous-time LTI system, $$\mathcal{G} : \mathcal{L}_{2e} \rightarrow \mathcal{L}_{2e}$$, with minimal state-space relization (A, B, C, D), where $$\mathcal{A} \in \mathcal{R}^{n\times n}, \mathcal{B} \in \mathcal{R}^{n\times m}, \mathcal{C} \in \mathcal{R}^{p\times n},$$ and $$\mathcal{D} \in \mathcal{R}^{p\times m} $$.

\begin{align} \dot x(t)&=Ax(t)+Bu(t),\\ y(t)&=Cx(t)+Du(t)\\ \end{align}$$

The Data
The matrices The matrices $$ A,B,C $$ and $$D $$

The Optimization Problem
The system $$\mathcal{G}$$ is QSR disipative if

 * $$\int_0^T (y^T(t)Qy(t) + 2y^TSu(t) + u^T(t)Ru(t))\,dt \ge 0, \forall u \in \mathcal{L}_{2e}, \forall T \ge 0 $$

where $$u(t)$$ is the input to $$\mathcal{G}, y(t)$$ is the output of $$\mathcal{G}, Q \in \mathcal{S}^{p}, S \in \mathcal{R}^{p\times m},$$ and $$\mathcal{R} \in \mathcal{S}^{m}$$.

LMI : KYP Lemma for QSR Dissipative Systems
The system $$\mathcal{G}$$ is also QSR dissipative if and only if there exists $$ P \in \mathcal{S}^{n},$$ where $$ P > 0,$$ such that

 * $$\begin{bmatrix}

PA + A^{T}P - C^{T}QC & PB - C^{T}S - C^{T}QD \\ (PB - C^{T}S - C^{T}QD)^{T} &  -D^{T}QD - (D^{T}S + S^{T}D) - R \end{bmatrix}\le 0.$$

title: User:Vasenthi/sandbox


text:
LMIs in Control/LMI Matrix Properties

Contents

 * /Maximum Singular Value of a Complex Matrix/

 * /Minimum Singular Value of a Complex Matrix/

 * /Minimization of Maximum Eigenvalue of a Matrix/

title: LMIs in Control/LMI Matrix Properties


text:
LMIs in Control/LMI Matrix Properties/Maximum Singular Value of a Complex Matrix

Maximum Singular Value of a Complex Matrix

The System
Consider $$ A \in \mathbb{R}^{n \times m} $$ as well as $$ \gamma $$. A maximum singular value of a matrix $$ A $$ is less than $$ \gamma $$ if and only if $$ AA^H < \gamma^2I $$, where $$ A^H $$ is the conjugate transpose or Hermitian transpose of the matrix $$ A $$.

The Data
The matrix $$ A $$ is the only data required.

The LMI: Maximum Singular Value of a Complex Matrix
Using the Shur complement procedure, the following LMIs can be constructed:

\begin{align} \bar{\sigma}(A) < \gamma\\ \begin{bmatrix} \gamma I & A \\ A^H & \gamma I\end{bmatrix}&>0\\ \end{align}$$

The following LMI is also equivalent:

\begin{align} \bar{\sigma}(A) < \gamma\\ \begin{bmatrix} \gamma I & A^H \\ A & \gamma I\end{bmatrix}&>0\\ \end{align}$$

Conclusion:
The results from this LMI will give the maximum complex value of the matrix $$ A $$:

\begin{align} \bar{\sigma}(A) < \gamma \end{align}$$

Implementation
A link to CodeOcean or other online implementation of the LMI

Related LMIs

 * [\\ Minimum singular value of a complex matrix]


text:
Lentis/Oil Palm Plantations

Introduction
Oil palm plantations produce a vegetable oil from oil palms such as the African Elaeis guineensis. Crude palm oil is made from squeezing the fruit of an oil palm while while palm kernel oil comes from crushing the kernel of the fruit. Palm oil may be used in various everyday products including ice cream, packaged bread, margarine, lipstick, soap, laundry detergent, and bio-fuel.

The top three global exporters of palm oil are Indonesia, Malaysia, and the Netherlands. Both Indonesia and Malaysia are home to topical forests, home to diverse ecosystems. Palm oil exports are key components to the nations' economies.

The Roundtable on Sustainable Palm Oil (RSPO) is a group that unites participants in the palm oil industry. The RSPO consists of many participants involved in the palm oil production process, such as oil palm producers, processors, consumer goods manufacturers, retailers, and environmental and social non-governmental organizations (NGOs). One key function of the RSPO is to regulate how oil palm plantations are established and function. In the past, there has been specific focus on regulating and enforcing ethical practices of oil palm plantations in developing countries.

Deforestation
The popularity of palm oil in the global economy has encouraged the introduction of oil palm plantations in Indonesia and other tropical countries. In turn, mass deforestation has been prevalent in these countries in recent years. For example, 9 million hectares of Indonesian primary forests have been lost from 2002 to 2018.

Deforestation for oil palm plantations destroys the vibrant ecosystems of Southeastern Asia. For example, the forests of Malaysia and Indonesia are home to orangutans, an endangered group of great apes. The main threat to the survival of orangutan populations is the expansion of oil palm plantations in these countries. As forests are cleared out, orangutans lose their homes and food sources. Often, orangutans will be killed as agricultural pests invading these plantations. Wildlife conservation groups like the National Wildlife Federation have pressed the RSPO to expand their conservation efforts to help preserve the endangered species in these regions.

Deforestation has a large impact on the climate as well; Indonesian rainforests rival the Amazon forest in carbon content. Indonesian and Malaysia also contains the world’s large percentage of peat, or decayed organic matter, in their forests. The peat in these forests contain at least 18 times as much carbon than the trees above them, making them key factors to these forests’ carbon pools. Deforestation in these countries risks increasing global carbon emissions. One of the leading concerned groups is the Union of Concerned Scientists, which pushes for stricter regulations of conservation for these forests. In the past, the Union of Concerned Scientists has criticized the RSPO for not strictly protecting the forests of nations like Indonesia. Specifically, policies set by the RSPO protected primary (undisturbed) forests, but not others types like disturbed forests. The criticality of peatlands was also ignored for a long time. In response, in November 2018, the RSPO updated its Sustainability Principles and Criteria to forbid further deforestation or peatland usage.

Regulation alone is not enough to fully curb the effects of deforestation. A 2018 study found that RPSO-compliant plantations did not perform significantly better than non-compliant plantations. Plantations were evaluated based on metrics such as deforestation rates, carbon emissions, and orangutan death rates. While regulations mitigate further environmental damage, many plantations have already damaged forests in Indonesian and Malaysia. The study also claims that regulations for oil palm plantations have not been strictly enforced in the past. The global demand for palm oil will remain high, since palm oil is still used in a wide variety of products. In turn, oil palm plantations will continue to develop throughout tropical areas.

Bio-Fuels
As concerns about the risk of fossil fuels rise, many countries have begun taking steps towards renewable alternatives. The United Nation’s Sustainable Development Goals for 2015 to 2030 commits its members to adopting affordable and clean energy. To this end, many countries in the EU have started using bio-fuels as an alternative fuel source to fossil fuels. Due to palm oil's popularity, it is widely used in these bio-fuels. From 2015 to 2019, nearly half of the EU’s imported palm oil was used for bio-fuel. Studies have found that the environment damage done by encouraging the production of palm oil outweighs the benefits of not using fossil fuels. In response, the EU has motioned to stop subsidizing palm oil imports by 2020 and to phase out its use entirely by 2030. As the demand for palm oil subsides in the EU, the incentive for new palm oil plantations will diminish.

Labor

The palm oil industry is estimated to be worth 60 billion USD. However, plantations workers may struggle to earn enough to live on, with some only make 2.50 USD per day.

Due to low wages and high target quotas, palm oil harvesters often bring unofficial workers with them to help meet harvest quotas. The employed harvesters bear the costs of paying for their own and the unofficial workers' tools, injuries, and wages. Some of the unofficial workers are the workers' children. The plantations benefit from the child labor without having to employ or be responsible for them. Most of the child workers are teenagers, but some are elementary school aged. Plantation owners try to prevent child labor and shift to blame to plantation workers with warning signs and letters. However, these methods do not work well and the root cause is not addressed. Seasonal workers are paid below minimum wage. Nontransparent wage deductions and unpaid overtime are common. The combination of quotas, wage deductions, low wages, and employees covering their owns costs puts many workers into debt bondage. Plantation workers often have to submit their passports, work permits, and visas to their employers. This prevents workers from being able to legally leave the plantations.

Indofood is a large oil palm plantation company with human rights complaints against it. Their goal is to produce palm oil in a sustainable manner. In 2016, Indofood released a sustainability report. In it, they claimed to be on track for 100% sustainable palm oil by 2020. They also claimed to be on track for all plantations to be RSPO certified by the end of 2019. Baseline occupational health and safety programs should be in place by the end of 2017 with 89% of locations meeting the program standards at the end of 2016. Indofood stated they are dedicated to human and labor rights by working with local labor unions and workers to determine what a fair quota is, paying above the minimum wage, paying seasonal workers fairly, and working to prevent child labor.

The RSPO has made rules that companies must follow in order to have certified sustainable palm oil. The Rainforest Action Network (RAN) works to preserve forests, protect the climate, and uphold human rights in areas with rainforests such as Indonesia. Organisasi Penguatan dan Pengembangan Usaha-usaha Kerakyatan (OPPUK) works to resolve social, political, human rights, and environmental issues in Indonesia. The International Labor Rights Forum (ILRF) works to advance human rights for workers. Together, RAN, OPPUK, and ILRF submitted a complaint to RSPO about Indofood violating workers' human rights. After investigation, Indofood was removed from RSPO.

Nestlé produces secondary goods using palm oil. Nestlé is looking to use sustainable palm oil in order to promote smallholders and human rights. As of 2018, 64% of their palm oil used was sustainable. They are aiming to have 100% sustainable palm oil by 2020. Nestlé is taking action towards this goal. They have cut ties with 10 palm oil producers, including Indofood, who do not meet the sustainability standards. Nestlé cut ties with Indofood due to human rights issues. This happened before Indofood was removed from RSPO, but is due to the some of the same complaints against Indofood. Nestlé is just one example of companies which have stopped sourcing palm oil from unsustainable producers due to human rights issues. Other companies include Musim Mas and PepsiCo.

There are many consumers of secondary goods who wish for them to be palm oil free or to use sustainably sourced palm oil. One way they work towards this goal is with petitions. The petitions are often for specific companies to cut ties with conflict palm oil or for governments to start putting more regulations on products containing palm oil. Some of the petitions have over 100,00 signatures. In addition, some petitions focus on the human rights issues associated with sustainable palm oil.

Displacement
Oil palm plantations need space to operate and land acquisition can impact communities. This is an issue in Indonesia. Indonesian indigenous people occupy 40 to 70 million hectares of land while the Indonesian government only recognizes 1 million hectares of that land. As a result, many indigenous people are unaware when oil palm companies buy rights to their land from the government. They are only informed when the companies come to their land and begin using it. Indigenous people protest this practice to try to preserve ownership of their culturally significant land. They believe that these companies are stealing their land and the resources associated with the land.

Guatemala, the 6th top exporter of palm oil, also has instances of displaced communites. Lorenzo Pérez Mendoza, coordinator of the National Council of the Displaced in Guatemala (CONDEG), a non-government organization, has said that "communities are currently suffering a second displacement, which is forced in most cases, provoked by oil palm plantation companies." . This is another instance of oil palm companies coming into a region causing communities to be displaced out of the land they have traditionally owned.

Legacy Colonialism
Indonesia was ruled by the Dutch Empire, from 1815 to the early to mid 1900s, with the goal of making a self-supporting colony. During this time, an island called Sumatra had a large economic expansion due to the adoption of the new and popular plantation economy. Around 70 percent of today's Indonesian oil palm plantations are located on Sumatra, mainly due to the infrastructure that was built under the Dutch rule. The Netherlands, a territory that was part of the Dutch Empire, is the top European importer of palm oil. The Netherlands imports the majority of its palm oil from Indonesia. This relationship between Indonesia and The Netherlands may be a neo-colonialism relationship that is influenced by the Dutch colonialism of Indonesia.

Conclusion
Oil Palm Plantations are a reminder that modern day colonialism exists and is prevalent. Primary good production companies make large profits by extracting resources from countries and paying the workers low wages. In these countries, there are few other options for work, so the people are stuck with the working for the primary good production companies.

While secondary goods producers cut ties with palm oil producers over human rights and sustainability issues, the secondary goods producers may also have been influenced by their consumers. They may have chosen to cut ties with conflict palm oil in order to prevent loss of customers and maintain a good image. This can be extended beyond palm oil. In some cases, companies may use ethics as a manifest function with maintaining customers and keeping a good reputation as latent function.

Oil palm plantation companies have affected indigenous communities. Companies can legally take land that is not recognized by the government from indigenous people. This process ignores the views of indigenous people. This can be viewed as modern day colonialism. Land and resources are being taken which causes the value of the region to decrease.

Regulation is important for curbing negative effects, as is the case for oil palm plantations. However, instead of mitigating the effects, it may be more effective to look at the causes. As EU countries phases out the use of palm oil, the demand of palm oil will decrease. In turn, the creation of new palm oil plantations and the spread of their effects will slow.

Future research on this chapter may include deeper research into the legacy colonialism, the history of palm oil (such as why it became widespread), what properties of palm oil make it useful, labor conditions beyond Indonesia, and potential issues with uses of palm oil aside from bio-fuel.

title: Lentis/Oil Palm Plantations


text:
Talk:Lentis/Oil Palm Plantations

Potential sources (or at least they give us an idea of things we can look for):
 * https://www.ucsusa.org/resources/palm-oil
 * Criticizes RSPO for not regulating heavily enough
 * Only protects primary forests, not secondary, disturbed, regenerating forests
 * Doesn't fully protect Peatlants (see below)
 * Argues that FDA ban on artificial trans fat can increase demand for palm oil as an alternative
 * Ban was originally planned for 2018, but has been moved to 2020 at the moment
 * https://onlinelibrary.wiley.com/doi/abs/10.1111/gcb.12635
 * Claims that Indonesian forests rival Amazon forest in terms of carbon emissions
 * Might be useful to talk about why deforestation from Palm Oil Plantation is important
 * https://www.worldwildlife.org/industries/palm-oil
 * http://humanityunited.org/pdfs/Modern_Slavery_in_the_Palm_Oil_Industry.pdf
 * https://rspo.org/files/download/6af742e8d301975
 * http://indofoodagri.listedcompany.com/misc/sr2016.pdf
 * https://www.fda.gov/food/food-additives-petitions/trans-fat
 * Trans-fats being phased out in US could increase demand of Palm Oil
 * https://www.rainforest-rescue.org/topics/palm-oil
 * NPO who focuses on deforestation effects of palm oil. According to their page, in EU majority of palm oil is used as fuel
 * https://www-pnas-org.proxy01.its.virginia.edu/content/116/38/19193.full
 * Recent paper on how palm oil plantations limitations might not affect deforestation that much
 * Also discusses how regulation may be less effective when considering how it interacts with global markets
 * https://www.researchgate.net/publication/227694185_Page_SE_Rieley_JO_and_Banks_CJ_Global_and_regional_importance_of_the_tropical_peatland_carbon_pool_Glob_Change_Biol
 * Peatlands- swampy land below forests (hold 18-28 times more carbon than forests above them; need to fact-check this stat)
 * https://www.youtube.com/watch?v=agSkTJKCfRE
 * Documentary video which discusses how indigenous groups are affected by palm oil production/farming

Thoughts (without having done too much research yet):
 * Could there be some colonialism here like with the cobalt miners?
 * there is a lot to look into with deforestation and labor rights
 * food vs fuel? Maybe this does not fall into plantations

-

What I want to write about next (and some useful sources?): General STS: --- Manifest and latent functions? For example, look into the the reasons pepsico and other companies say they cut ties with unsustainable palm oil.... however, also look into the petitions for these companies to do so. Manifest: sustainability/good practices... latent: customers?
 * petitions from consumers for sustainable palm oil
 * the abuse of palm oil workers is still prevalent. Palm oil is being taken out of indonesia and the companies that use/sell it are making the big bucks while the workers face low wages and poor conditions. This is modern day colonialism at work.
 * Earning little with business size... colonialism: https://www.amnesty.org/en/latest/news/2016/11/key-facts-about-palm-oil/

Ss3fg (discuss • contribs) 03:19, 1 November 2019 (UTC)

--- Look into how deforestation has affected wild fires in Indonesia --Kml9pw (discuss • contribs) 18:49, 9 November 2019 (UTC) --- Environmental link: https://www.spott.org/palm-oil-resource-archive/impacts/environmental/

Social link: https://www.spott.org/palm-oil-resource-archive/impacts/social/

Rcr4eh (discuss • contribs) 17:58, 9 November 2019 (UTC)

title: Talk:Lentis/Oil Palm Plantations


text:
LMIs in Control/Parametric, Norm-Bounded Uncertain System Quadratic Stability (dual version)

The System

\begin{align} \dot x(t)&=Ax(t)+Mp(t),&&p(t) = \Delta (t)q(t),\\ q(t) &= Nx(t)+Qp(t),&&\Delta \in \mathbf{\Delta} \; := \{\Delta \in \mathbb{R}^{n \times n} : \| \Delta \| \leq 1 \}\\ \end{align}$$

The Data
The matrices $$ A,M,N,Q $$.

The LMI: The Lyapunov Inequality

\begin{align} \text{Find} \; &P>0,\mu \geq 0:\\ \begin{bmatrix} AP+PA^T & PN^T \\ NP & 0\end{bmatrix} + \mu \begin{bmatrix} MM^T & MQ^T \\ QM^T & QQ^T - I \end{bmatrix} < 0\\ \end{align}$$

Conclusion:
The system above is quadratically stable if and only if there exists some mu >= 0 and P > 0 such that the LMI is feasible. This LMI is a good way to determine quadratic stability of a system with parametric, norm-bounded uncertainty.

Implementation
A link to CodeOcean or other online implementation of the LMI

Related LMIs
Links to other closely-related LMIs


text:
User:Harishankar Prabhakaran

Discrete-Time Mixed H2-H∞-Optimal Full-State Feedback Control

A discrete time system operates on a discrete time signal input and produces a discrete time signal output. They are used in digital signal processing, such as digital filters for images or sound. The class of discrete time systems that are both linear and time invariant, known as discrete time LTI systems.

A full-state feedback controller $$K = K_d \in {R^{n_u*n_x}}$$ (i.e., $$uk = K_dx_k$$) is to be designed to minimize the H2 norm of the closed loop transfer matrix $$T11(z)$$ from the exogenous input $$w_{1,k}$$ to the performance output $$z_{1,k}$$ while ensuring the H∞ norm of the closed-loop transfer matrix $$T22(z)$$ from the exogenous input $$w_{2,k}$$ to the performance output $$z_{2,k}$$ is less than $$\gamma_{d}$$.

The System
Discrete-Time LTI System with state space realization

$$ \begin{align}

x_{k+1}&=A_{d}x_{k}+B_{d1,1}w_{1,k}+B_{d1,2}w_{2,k}+B_{d2}u_{k},\\

\begin{bmatrix} Z_{1,k}\\ Z_{2,k}\end{bmatrix} &= \begin{bmatrix} C_{d1,1}\\ C_{d1,2}\end{bmatrix}x_{k}+ \begin{bmatrix} 0 & D_{d11,12}\\ D_{d11,21} & D_{d11,22}\end{bmatrix} \begin{bmatrix} w_{1,k}\\ w_{2,k}\end{bmatrix}+ \begin{bmatrix} D_{d12,1}\\ D_{d12,2}\end{bmatrix}u_{k}\\

y_k &= x_k\\ \end{align} $$

The Data
The matrices: System $$ (A_d,B_{d1,1},B_{d1,2},B_{d2},C_{d1,1},C_{d1,2},D_{d11,12},D_{d11,21},D_{d11,22},,D_{d12,1},D_{d12,2}), P, F_d $$.

The Optimization Problem
The following feasibility problem should be optimized:

Minimize the H2 norm of the closed loop transfer matrix T11(z), while ensuring the H∞ norm of the closed-loop transfer matrix T22(z) is less than $$\gamma_{d}$$, while obeying the LMI constraints.

The LMI:
Discrete-Time Mixed H2-H∞-Optimal Full-State Feedback Controller is synthesized by solving for $$P \in S^{n_{x}}, Z \in S^{n_{w}}, F_{d} \in R^{n_{u} * n_{x}}$$, and $$\mu \in R_{>0}$$ that minimize $$\mu$$ subject to $$P>0, Z>0$$

The LMI formulation

H∞ norm < $$\gamma_{d}$$

H2 norm < $$\mu$$

$$ \begin{align}

\begin{bmatrix}P & A_{d}P-B_{d2}F_{d} & B_{d1,1}\\
 * & P & 0\\
 * & * & 1\end{bmatrix}&>0\\

\begin{bmatrix}P & A_{d}P-B_{d2}F_{d} & B_{d1,2} & 0\\
 * & P & 0 & PC_{d1,2}^T-F_{d}^TD_{d12,2}^T\\
 * & * & \gamma_{d} I & D_{d11,22}^T\\
 * & * & * & \gamma_{d} I\end{bmatrix}&>0\\

\begin{bmatrix} Z & C_{d1,1}P-D_{d12,1}\\
 * & P\end{bmatrix}&>0\\

trace(Z) &< \mu^2

\end{align}$$

Conclusion:
The H2-optimal full-state feedback controller gain is recovered by $$K_{d}=F_{d}P^{-1}$$

Implementation
A link to CodeOcean or other online implementation of the LMIMATLAB Code

Related LMIs
Continuous_Time_Lyapunov_Inequality - Lyapunov_Inequality

title: User:Harishankar Prabhakaran


text:
User:LBird BASc/sandbox/ATK/Seminar6/Power/Power in International Relations

Power in International Relations
Power is a concept which affects a multitude of disciplines. One of the most common perceptions of power is found in world politics and International Relations, since it affects the way states interact and why wars happen. Power will be looked at through three main perspectives in International Relations: realism, liberalism and constructivism.

Realism The realist stream of thought perceives the state behaviour is reflective of human nature, which is inherently power-seeking and centered around increasing security. Thus, states will act competitively and aggressively towards each other in the anarchical structure of the world arena. This viewpoint became popular after the events of the First and Second World Wars. Neorealism follows the same logic of self-help, however it puts more emphasis on the anarchical structure of the world, which directly causes this type of state behaviour. Finally, according to neorealism states will always seek to become the hegemon (have the maximum power) or at least reach a balance of power. For realists, power is defined mainly by military strength, wealth and population size.

Liberalism

The liberalist perspective is much more positive about state relations and power. Liberals can be considered idealist due to their hopeful view of the world and cooperation between countries and institutions. From this point of view, democratic states are the most powerful, especially since cooperation between democracies is more likely to occur leading to collective security and free economic trade. An example is the European Union. Furthermore, an emphasis on globalisation shows how all countries are interconnected and therefore power can be spread more equally, whilst the liberalisation of countries will lead to peace since they would not seek more power due to their wealth.

Constructivism

Constructivism looks at the influence of ideas, social norms and context, analysing the relationship between agent and structure. From this perspective, the idea of power is much more fluid, which can be changed and altered as time goes by. Therefore, our changing definition of what power means will affect the way states interact, and in turn the context will also affect our definition of power and behaviour. Therefore, social constructions play a crucial role in defining power, which will affect the way countries interact.


text: User:La coince

title: User:La coince


text: User:LGreg/sandbox/Approaches to Knowledge (LG seminar)/Group 2/Power/Power and the environment


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LMIs in Control/Discrete-Time Algebraic Riccati Inequality (DARE)

The System
Consider a Discrete-Time LTI system

\begin{align} x_{k+1} = A_dx_k + B_du_k \end{align}$$

\begin{align} y_k = C_dx_k \end{align}$$

Consider $$A_d \in\mathbb{R}^{n\times n}; B_d\in\mathbb{R}^{n\times m}$$

The LMI: Discrete-Time Algebraic Riccati Inequality (DARE)
An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time

The Discrete-Time Algebraic Riccati Inequality is given by

\begin{align} A_d^TPA_d - A_d^TPB_d (R + B_d^TPB_d)^{-1} B_d^TPA_d + Q - P \geq 0 \end{align}$$

$$P, Q\in\mathbb{S}^n$$ and $$R\in\mathbb{S}^m$$ where $$P > 0, Q \geq 0, R > 0$$.

$$P$$ is the unknown n by n symmetric matrix and $$A, B, Q, R$$ are known real coefficient matrices.

The above equation can be rewritten using the Schur Complement Lemma as:

\begin{bmatrix} A_d^TPA_d-P+Q & A_d^TPB_d \\ B_d^TPA_d & R+B_d^TPB_d \end{bmatrix}$$$$\begin{align}\geq 0\end{align}$$

The Data
The Matrices $$A_d, B_d, C_d, Q, R$$ are given

$$Q$$ and $$R$$ should necessarily be Hermitian matrices.

A square matrix is Hermitian if it is equal to its complex conjugate transpose.

The Optimization Problem
Our aim is to find

$$P$$ - Unique solution to the discrete-time algebraic Riccati equation, returned as a matrix.

$$K$$ - State-feedback gain, returned as a matrix.

The algorithm used to evaluate the State-feedback gain is given by

\begin{align} K = (R+B_d^TPB_d)^{-1}B_d^TPA_d \end{align}$$

$$L$$ - Closed-loop eigenvalues, returned as a matrix.

Conclusion:
Algebraic Riccati Inequalities play a key role in LQR/LQG control, H2- and H∞ control and Kalman filtering. We try to find the unique stabilizing solution, if it exists. A solution is stabilizing, if controller of the system makes the closed loop system stable.

Equivalently, this Discrete-Time algebraic Riccati Inequality is satisfied under the following necessary and sufficient condition:

\begin{bmatrix} Q & 0 & A_d^TP & P\\ 0 & R & B_d^TP & 0\\ PA_d & PB_d & P & 0\\ P & 0 & 0 & P \end{bmatrix}$$$$\begin{align}\geq 0\end{align}$$

Implementation
($$X$$ in the output corresponds to $$P$$ in the LMI)

A link to the Matlab code for a simple implementation of this problem in the GitHub repository:

https://github.com/yashgvd/ygovada

Related LMIs
LMI for Continuous-Time Algebraic Riccati Inequality

LMI for Schur Stabilization


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LMIs in Control/Stability Analysis/LMI for the Continuous-Time D-Stability Controller

../../pages/Continuous_Time_D-Stability_Controller


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LMIs in Control/Stability Analysis/Parametric, Norm-Bounded Uncertain System Quadratic Stability

The System

\begin{align} \dot x(t)&=Ax(t)+Mp(t),&&p(t) = \Delta (t)q(t),\\ q(t) &= Nx(t)+Qp(t),&&\Delta \in \mathbf{\Delta} \; := \{\Delta \in \mathbb{R}^{n \times n} : \| \Delta \| \leq 1 \}\\ \end{align}$$

The Data
The matrices $$ A,M,N,Q $$.

The LMI: The Lyapunov Inequality

\begin{align} \text{Find} \; &P>0,\mu \geq 0:\\ \begin{bmatrix} AP+PA^T & PN^T \\ NP & 0\end{bmatrix} + \mu \begin{bmatrix} MM^T & MQ^T \\ QM^T & QQ^T - I \end{bmatrix} < 0\\ \end{align}$$

Conclusion:
The system above is quadratically stable if and only if there exists some mu >= 0 and P > 0 such that the LMI is feasible. This LMI is a good way to determine quadratic stability of a system with parametric, norm-bounded uncertainty.

Implementation
https://github.com/mcavorsi/LMI

Related LMIs
Stability of Structured, Norm-Bounded Uncertainty

Stability under Arbitrary Switching

Quadratic Stability Margins


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LMIs in Control/Tools/Elimination of Variables

 * /Variable Elimination in a Partition Matrix/
 * /Schur Complement/
 * /Elimination of Variables/


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LMIs in Control/Stability Analysis/LMI for the Continuous-Time D-Stability Observer

../../pages/Continuous_Time_D-Stability_Observer


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LMIs in Control/LMIs for Hurwitz Stability

This is a set of LMI conditions for determining Hurwitz Stability of continuous time systems.

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t),\\ y(t)&=Cx(t)+Du(t)\\ \end{align}$$

The Data

 * The matrices $$ A,B,C,D $$ are system matrices of appropriate dimensions.
 * $$ x \in \mathbb{R}^n $$, $$y \in \mathbb{R}^m$$ and $$u \in \mathbb{R}^r $$ are state vector, output vector and input vector respectively.

The Optimization Problem
Find a symmetric postive definite matrix $$X$$, where $$X \in \mathbb{R}^n$$. Thus $$ X>0 $$ and $$K = ZX^{-1} $$ where $$Z \in \mathbb{R}^r$$.

The LMI: The Lyapunov Inequality
Matrix pair $$(A,B)$$, is Hurwitz stabilizable if and only if there exist a symmetric positive definite matrix $$X$$ and a matrix $$Z$$ satisfying

$$AX + XA^T + BZ + Z^{T}B^T < 0$$

Proof : Matrix pair $$(A,B)$$, is Hurwitz stabilizable if and only if

$$rank[sI - A  B] = n $$, $$\forall s \in \lambda (A)  $$ and $$Re(s) \ge 0$$

This is the definition of Hurwitz Stability. Now, using this definition we can prove the above LMI if we find matrix $$X > 0$$ and matrix $$Z$$ and thus by substituting $$Z = KX$$ in the above LMI we get,

$$(A+BK)X + X(A+BK)^{T} < 0 $$, which brings us to the Lyapunov Stability Theory.

Conclusion:
Thus by proving the above conditions we prove that the matrix pair $$(A,B)$$ is Hurwitz Stabilizable. At the same time, we also prove that the $$ rank[sI-A B] = n$$ i.e. it is full rank and the real part of $$s$$ is $$ > 0 $$.

Implementation
Please find the MATLAB implementation at this link below https://github.com/omiksave/LMI

Related LMIs
Links to other closely-related LMIs

 * Schur Stability
 * Quadratic Hurwitz Stability
 * Quadratic Schur Stability
 * Quadratic D-Stability

Return to Main Page:

 * https://en.wikibooks.org/wiki/LMIs_in_Control


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LMIs in Control/Tools/Elimination of Variables/Variable Elimination in a Partition Matrix

WIP, Description in progress

Two basic lemmas treat the elimination of variables in a partitioned matrix.

Lemma 1
Consider the matricies $$Z=\begin{bmatrix} Z_{11} & Z_{12} \\ Z_{12}^T & Z_{22} \end{bmatrix} $$, $$Z_{11}\in\mathbb{R}^{n\times n}$$, be symmetrix. Then, there exists a symmetric matrix $$ X $$ such that

$$ \begin{bmatrix} Z_{11}-X & Z_{12} & X \\ Z_{12}^T & Z_{22} & 0 \\ X & 0 & -X \end{bmatrix} < 0 $$

if and only if

$$Z=\begin{bmatrix} Z_{11} & Z_{12} \\ Z_{12}^T & Z_{22} \end{bmatrix} < 0 $$.

Lemma 2
Let $$Z_{ij}$$, $$i=1,2,3,j=i,\cdots,3$$, be given matrices of appropriate dimensions. Then there exists a matrix $$X$$ such that

$$ \begin{bmatrix} Z_{11} & Z_{12} & Z_{13} \\ Z_{12}^T & Z_{22} & Z_{23}+X^T \\ Z_{13}^T & Z_{23}^T+X & Z_{33} \end{bmatrix} < 0 $$

if and only if

$$Z=\begin{bmatrix} Z_{11} & Z_{12} \\ Z_{12}^T & Z_{22} \end{bmatrix} < 0 $$, $$Z=\begin{bmatrix} Z_{11} & Z_{13} \\ Z_{13}^T & Z_{33} \end{bmatrix} < 0 $$

In this case, $$X$$ is given by

$$X=Z_{13}^TZ_{11}^{-1}Z_{12}-Z_{23}^T$$.

WIP, additional references to be added


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LMIs in Control/Discrete-Time Systems

Discrete-Time systems

 * /Discrete-Time Lyapunov Stability/
 * /Discrete-Time H2-Optimal Observer/
 * /Discrete-Time H∞-Optimal Observer/
 * /Discrete-Time Mixed H2-H∞-Optimal Observer/
 * /Discrete-Time Algebraic Riccati Inequality (DARE)/

title: LMIs in Control/Discrete-Time Systems


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LMIs in Control/Discrete-Time Systems/Discrete-Time Lyapunov Stability

Discrete-Time Lyapunov Stability

The System
Discrete-Time System

\begin{align} x(t)_{k+1}&=A_dx(t)_k,&A_d \in \bf{R^{n*n}} \;\\ \end{align}$$

The Data
The matrices $$ System A_d,P $$.

The Optimization Problem
The following feasibility problem should be solved:

Find P obeying the LMI constraints.

The LMI:
Discrete-Time Lyapunov Stability

The LMI formulation

\begin{align} P \in \bf{S^{n}}\\ Find \; &P>0,\\ \begin{bmatrix} A_d^T P A_d - P\end{bmatrix}&\leq0 \end{align}$$

Conclusion:
If there exists a $$P \in \bf{S^{n}}$$ satisfying the LMI then, $$|\lambda_i(A_d)|\leq 1, \forall i = 1,2,...,n;$$ and the equilibrium point $$\bar{x}=0$$  of the system is Lyapunov stable.

Implementation

 * [] - MATLAB implementation of the LMI.

Related LMIs
Continuous_Time_Lyapunov_Inequality - Lyapunov_Inequality


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LMIs in Control/LMI Matrix Properties/Minimization of Maximum Eigenvalue of a MAtrix

The System

\begin{align} A(x) = A_{0}+A_{1}x_{1}+ ... + A_{n}x_{n} \end{align}$$

Note that $$ \begin{align} A_{i}, \quad i=1, 2, ..., n \end{align}$$ are symmetric matrices.

The Data

\begin{align} A_{0}, A_{1}, ..., A_{n} \quad \text{are given matrices.} \end{align}$$

The Optimization Problem
Find

$$\begin{align} x = [x_{1} \quad x_{2} ... x_{n}] \end{align}$$

to minimize,

$$\begin{align} J(x) = \lambda_{max}(A(x)) \end{align}$$

According to Lemma 1.1 in [1] page 10, the following statements are equivalent

$$\begin{align} \lambda_{max}(A(x)) \leq t \iff A(x)-tI \leq 0 \end{align}$$

The LMI: The Lyapunov Inequality
Title and mathematical description of the LMI formulation.

\begin{align} \text{min} \; \quad t:&\\ \text{s.t.} \quad \begin{bmatrix} A(x)-tI \end{bmatrix}& \leq 0 \end{align}$$

Conclusion:
$$\begin{align} x_{i}, \quad i =1, 2, ... , n \quad \text{and} \quad t > 0 \end{align}$$ are parameters to be optimized

Implementation
A link to Matlab codes for this problem in the Github repository:

https://github.com/asalimil/LMI-for-Minimizing-the-Maximum-Eigenvalue-of-Matrix/blob/master/README.md

Related LMIs
LMI for Matrix Norm Minimization

LMI for Schur Stabilization


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LMIs in Control/LMI Matrix Properties/Minimization of Maximum Eigenvalue of a Matrix

The System

\begin{align} A(x) = A_{0}+A_{1}x_{1}+ ... + A_{n}x_{n} \end{align}$$

Note that $$ \begin{align} A_{i}, \quad i=1, 2, ..., n \end{align}$$ are symmetric matrices.

The Data

\begin{align} A_{0}, A_{1}, ..., A_{n} \quad \text{are given matrices.} \end{align}$$

The Optimization Problem
Find

$$\begin{align} x = [x_{1} \quad x_{2} ... x_{n}] \end{align}$$

to minimize,

$$\begin{align} J(x) = \lambda_{max}(A(x)) \end{align}$$

According to Lemma 1.1 in [1] page 10, the following statements are equivalent

$$\begin{align} \lambda_{max}(A(x)) \leq t \iff A(x)-tI \leq 0 \end{align}$$

The LMI: The Lyapunov Inequality
Title and mathematical description of the LMI formulation.

\begin{align} \text{min} \; \quad t:&\\ \text{s.t.} \quad \begin{bmatrix} A(x)-tI \end{bmatrix}& \leq 0 \end{align}$$

Conclusion:
$$\begin{align} x_{i}, \quad i =1, 2, ... , n \quad \text{and} \quad t > 0 \end{align}$$ are parameters to be optimized

Implementation
A link to Matlab codes for this problem in the Github repository:

https://github.com/asalimil/LMI-for-Minimizing-the-Maximum-Eigenvalue-of-Matrix/blob/master/README.md

Related LMIs
LMI for Matrix Norm Minimization


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LMIs in Control/Stability Analysis/Stability of Lure's Systems

The System

\begin{align} \dot x(t)&=Ax(t)+B_pp(t)+B_ww(t),\\ z(t)&=C_zx(t)\\ p_i(t)&=\phi_i(q_i(t)), i=1,\dots, n_p\\ q&=C_qx,\\ 0 &\leq \sigma \phi_i(\sigma) \leq \sigma^2 \ \forall \sigma \in \mathbb{R} \end{align}$$

The Data
The matrices $$ A,B_p,B_w,C_q,C_z $$.

The LMI: The Lure's System's Stability
The following feasibility problem should be solved as sufficient condition for the stability of the above Lur'e system.

\begin{align} \text{Find} \; &P>0,\Lambda=diag(\lambda_1,\dots,\lambda_{n_p})\succeq 0, T=diag(\tau_1,\dots,\tau_{n_p}) \succeq 0:\\ &\begin{bmatrix} A^\top P+PA & PB_p+A^\top C^\top_q \Lambda +C^\top_q T \\ B^\top_p P + \Lambda C_qA+TC_q & \Lambda C_q B_p+B^\top_p C^\top_q \Lambda-2T \end{bmatrix} \prec 0\\ \end{align}$$

Implementation
https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/9030b507b39f658fb34fef8563ce9130d5dc2baa https://codeocean.com/capsule/0232754/tree

Conclusion
If the feasibility problem with LMI constraints has solution, then the Lure's system is stable.

Remark
The LMI is only a sufficient condition for the existence of a Lur’e Lyapunov function that proves stability of Lur'e system. It is also necessary when there is only one nonlinearity, i.e., when $$ n_p = 1 $$.


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LMIs in Control/Stability Analysis/Hurwitz Stability

This is a set of LMI conditions for determining Hurwitz Stability of continuous time systems.

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t),\\ y(t)&=Cx(t)+Du(t)\\ \end{align}$$

The Data

 * The matrices $$ A,B,C,D $$ are system matrices of appropriate dimensions.
 * $$ x \in \mathbb{R}^n $$, $$y \in \mathbb{R}^m$$ and $$u \in \mathbb{R}^r $$ are state vector, output vector and input vector respectively.

The Optimization Problem
Find a symmetric postive definite matrix $$X$$, where $$X \in \mathbb{R}^n$$. Thus $$ X>0 $$ and $$K = ZX^{-1} $$ where $$Z \in \mathbb{R}^r$$.

The LMI: The Lyapunov Inequality
Matrix pair $$(A,B)$$, is Hurwitz stabilizable if and only if there exist a symmetric positive definite matrix $$X$$ and a matrix $$Z$$ satisfying

$$AX + XA^T + BZ + Z^{T}B^T < 0$$

Proof : Matrix pair $$(A,B)$$, is Hurwitz stabilizable if and only if

$$rank[sI - A  B] = n $$, $$\forall s \in \lambda (A)  $$ and $$Re(s) \ge 0$$

This is the definition of Hurwitz Stability. Now, using this definition we can prove the above LMI if we find matrix $$X > 0$$ and matrix $$Z$$ and thus by substituting $$Z = KX$$ in the above LMI we get,

$$(A+BK)X + X(A+BK)^{T} < 0 $$, which brings us to the Lyapunov Stability Theory.

Conclusion:
Thus by proving the above conditions we prove that the matrix pair $$(A,B)$$ is Hurwitz Stabilizable. At the same time, we also prove that the $$ rank[sI-A B] = n$$ i.e. it is full rank and the real part of $$s$$ is $$ > 0 $$.

Implementation
Please find the MATLAB implementation at this link below https://github.com/omiksave/LMI

Related LMIs
Links to other closely-related LMIs

 * Schur Stability
 * Quadratic Hurwitz Stability
 * Quadratic Schur Stability
 * Quadratic D-Stability

Return to Main Page:

 * https://en.wikibooks.org/wiki/LMIs_in_Control


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LMIs in Control/Tools/Maximum Singular Value of a Complex Matrix

Maximum Singular Value of a Complex Matrix

The System
Consider $$ A \in \mathbb{R}^{n \times m} $$ as well as $$ \gamma $$. A maximum singular value of a matrix $$ A $$ is less than $$ \gamma $$ if and only if $$ AA^H < \gamma^2I $$, where $$ A^H $$ is the conjugate transpose or Hermitian transpose of the matrix $$ A $$.

The Data
The matrix $$ A $$ is the only data required.

The LMI: Maximum Singular Value of a Complex Matrix
Using the Shur complement procedure, the following LMIs can be constructed:

\begin{align} \bar{\sigma}(A) < \gamma\\ \begin{bmatrix} \gamma I & A \\ A^H & \gamma I\end{bmatrix}&>0\\ \end{align}$$

The following LMI is also equivalent:

\begin{align} \bar{\sigma}(A) < \gamma\\ \begin{bmatrix} \gamma I & A^H \\ A & \gamma I\end{bmatrix}&>0\\ \end{align}$$

Conclusion:
The results from this LMI will give the maximum complex value of the matrix $$ A $$:

\begin{align} \bar{\sigma}(A) < \gamma \end{align}$$

Implementation

 * Maximum Singular Value Example

Related LMIs

 * Minimum singular value of a complex matrix


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LMIs in Control/Tools/Minimization of Maximum Eigenvalue of a Matrix

The System

\begin{align} A(x) = A_{0}+A_{1}x_{1}+ ... + A_{n}x_{n} \end{align}$$

Note that $$ \begin{align} A_{i}, \quad i=1, 2, ..., n \end{align}$$ are symmetric matrices.

The Data

\begin{align} A_{0}, A_{1}, ..., A_{n} \quad \text{are given matrices.} \end{align}$$

The Optimization Problem
Find

$$\begin{align} x = [x_{1} \quad x_{2} ... x_{n}] \end{align}$$

to minimize,

$$\begin{align} J(x) = \lambda_{max}(A(x)) \end{align}$$

According to Lemma 1.1 in [1] page 10, the following statements are equivalent

$$\begin{align} \lambda_{max}(A(x)) \leq t \iff A(x)-tI \leq 0 \end{align}$$

The LMI: Minimization of Maximum Eigenvalue of a Matrix
Mathematical description of the LMI formulation:

\begin{align} \text{min} \; \quad t:&\\ \text{s.t.} \quad \begin{bmatrix} A(x)-tI \end{bmatrix}& \leq 0 \end{align}$$

Conclusion:
$$\begin{align} x_{i}, \quad i =1, 2, ... , n \quad \text{and} \quad t > 0 \end{align}$$ are parameters to be optimized

Implementation
A link to Matlab codes for this problem in the Github repository:

https://github.com/asalimil/LMI-for-Minimizing-the-Maximum-Eigenvalue-of-Matrix

Related LMIs
LMI for Matrix Norm Minimization

LMI for Schur Stabilization


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LMIs in Control/pages/Algebraic Riccati Inequality

Algebraic Riccati Equations are particularly significant in Optimal Control, filtering and estimation problems. The need to solve such equations is common in the analysis and linear quadratic Gaussian control along with general Control problems. In one form or the other, Riccati Equations play significant roles in optimal control of multivariable and large-scale systems, scattering theory, estimation, and detection processes. In addition, closed forms solution of Riccati Equations are intractable for two reasons namely; one, they are nonlinear and two, are in matrix forms.

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t)\\ \end{align}$$

The Data
Following matrices are needed as Inputs:.

 * $$ A,B,N$$.

The Optimization Problem
In control systems theory, many analysis and design problems are closely related to Riccati algebraic equations or inequalities. Find

The LMI: Algebraic Riccati Inequality
Title and mathematical description of the LMI formulation.

\begin{align} P>0, \\Q>0, \\ R>0.\\ \text{ The Algebraic Riccati inequality is given by}\;\\ A^T P+PA - (PB+N^T)R^-1(B^TP+N)+Q & \geq 0\\ \\ \text{ can be written using the Schur complement lemma as}\;\\ \begin{bmatrix} A^TP+PA+Q && PB+N^T\\ \star && R\\ \end{bmatrix}& \geq 0 \end{align}$

Conclusion:
If the solution exists, LMIs give a unique, stabilizing, symmetric matrix P.

Implementation:
Matlab code for this LMI in the Github repository:

 * 1) REDIRECT []


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User:Omotarae/sandbox

The wiki code for bold text is like this:

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bold = bold

To link to an article with a different name than the text, put a | (a "pipe") in between the code and the word you want to appear on the page:

bold = bold (with the link to )

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Small text = subscript

Contents

To create a table of contents (use Heading, under Advanced). The table of contents is created automatically, but that allows you to give each heading some sense of hierarchy.

= Omotara Edu =

SSSI
Attended sssi from the age of 4 till 11. Ikoyi. International school ....

Grange
Two years. GPA system. Mrs Aderinto taught Geog...

DH
From the age of 13, Omotara attended Downe House School Downe House School, a boarding school in New...

UIV
First year ...

GCSEs
She studied .... at GCSE ...

A Level
Final two years ....

UCL
Uni at University College London

title: User:Omotarae/sandbox


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LMIs in Control/Discrete-Time Systems/Discrete-Time H2-Optimal Observer

The System

\begin{align}

x_{k+1}&=A_{d}x_{k}+B_{d1}w_{k},\\

y_{k}&=C_{c2}x_{k} + D_{d21}w_{k}\\ \end{align} $$

Where it is assumed that :$$(A_{d}, C_{d2})$$ is detectable.

The Data
The matrices $$ A_{d}, B_{d1}, C_{cd2}, C_{cd1}, D_{d21} $$.

The Optimization Problem
An observer of the form:

\begin{align}

\hat x_{k+1}&=A_{d}\hat x_{k}+ L_{d}(y_{k}-\hat y_{k}),\\

\hat y_{k}&=C_{d2} \hat x_{k} \\ \end{align} $$

is to be designed, where $$ L_{d} \in R^{n_{x} \times n_{y}}$$ is the observer gain.

Defining the error state $$ e_{k} = x_{k} - \hat x_{k}$$, the error dynamics are found to be

$$e_{k+1} = (A_{d} - L_{d}C_{d2} e_{k} + (B_{d1} - L_{d}D_{d21})w_{k}$$,

and the performance output is defined as

$$z_{k} = C_{d1}e_{k}$$.

The observer gain $$L_{d}$$ is to be designed such that the $$H_{2}$$ of the transfer matrix from $$w_{k}$$ to $$z_{k}$$, given by

$$L_{d} \begin{align} T(z) &= C_{d1}(z1 - (A_{d} - L_{d}C_{d2}))^{-1}(B_{d1} - L_{d}D_{d21}),\\ \end{align} $$

is minimized.

The LMI: Discrete-Time H2-Optimal Observer
The discrete-time $$H_{2}$$-optimal observer gain is synthesized by solving for $$P \in S^{n_{x}}$$, $$Z \in S^{n_{z}}$$, $$G_{d} \in R^{n_{x} \times n_{y}}$$, and $$v \in R_{>0}$$ that minimize $$J(v) = v$$ subject to $$P>0, Z>0$$,

\begin{align}

\begin{bmatrix}P & PA_{d}-G_{d}C_{d2} & PB_{d1}-G_{d}D_{d21}\\
 * & P & 0\\
 * & * & 1\end{bmatrix}&>0,\\

\begin{bmatrix} Z & PC_{d1}\\
 * & P\end{bmatrix}&>0,\\

\operatorname{tr}Z<v

\end{align}$$

Conclusion:
The $$H_{2}$$-optimal observer gain is recovered by $$L_{d} = P^{-1}G_{d}$$ and the $$H_{2}$$ norm of $$T(z)$$ is $$\mu = \sqrt{v}$$.

Implementation
https://github.com/rezajamesahmed/LMImatlabcode/blob/master/Discrete_Time_H2_Optimal_Observer_LMIs_Wikibook_Example.m

Related LMIs
Discrete-Time Mixed H2-H∞-Optimal Observer//

Discrete-Time H∞-Optimal Observer//


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LMIs in Control/LMI for Polytopic Uncertainity

 * /Polytopic Quadratic Stability/
 * /Quadratic Polytopic Hinf- Optimal State Feedback Control/


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LMIs in Control/Stability Analysis/Deduced LMI Conditions for H-infinity Index

H-infinity Index Deduced LMI

Although the KYP Lemma, also known as the /Bounded Real Lemma/, is a basic condition to evaluate an upper bound on the H∞, the verification of the bound on the H∞-gain of the system can be done via the deduced condition.

The System
A state-space representation of a linear system as given below:

\begin{align} \dot x(t)&=Ax(t)+Bw(t)\\ y(t)&=Cx(t)+Dw(t) \end{align}$$

where $$x(t)\in \R^n$$, $$y(t)\in \R^m$$ and $$w(t)\in \R^r$$ are the system state, output, and the disturbance vector respectively. The transfer function of such a system can be evaluated as:

\begin{align} G(s)=C(sI-A)^{-1}B+D \end{align}$$

The Data
Number of states n, number of outputs m and number of external noise channels r need to be known. Moreover, the system matrices A,B,C,D are also required to be known.

The Feasibility LMI
For an arbitrary $$ \gamma $$, the transfer function G(s) satisfies

 * $$ \left\| G(s) \right\|_{\infty} < \gamma $$

if and only if there exists a symmetric matrix X > 0 and a matrix $$ \Omega .$$ such that:

\begin{align} \text{Find} \; X, \Omega :&\\ \Theta + \Phi^\top \Omega \Psi + \Psi^\top \Omega^\top \Phi < 0 \end{align}$$

where:

\begin{align}

\Theta &= \begin{bmatrix} 0 & X & 0 & 0 & 0 \\ X & -X & 0 & 0 & 0 \\ 0 & 0 & -\gamma I_m & 0 & 0\\ 0 & 0 & 0 & -X & 0 \\ 0 & 0 & 0 & 0 & \gamma I_r \end{bmatrix} \\ \Phi &= \begin{bmatrix} -I_n & A^\top & C^\top & I_n & 0 \\ 0 & B^\top & D^\top & 0 & -\gamma I_r\end{bmatrix} \\ \Psi &= \begin{bmatrix} I_n & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & I_r\end{bmatrix} \end{align}$$

The above LMI can be combined with the bisection method to find minimum $$ \gamma $$ to find the minimum upper bound on the H∞ gain of $$ G(s) $$.

Conclusion:
If there is a feasible solution to the aforementioned LMI, then the $$ \gamma $$ upper bounds the infinity norm of the system G(s).

Implementation
To solve the feasibility LMI, YALMIP toolbox is required for setting up the feasibility problem, and SeDuMi is required to solve the problem. The following link showcases an example of the feasibility problem:

https://codeocean.com/capsule/1465618/tree

Related LMIs
/Bounded Real Lemma/


text:
LMIs in Control/KYP Lemmas

 * /KYP Lemma (Bounded Real Lemma)/
 * /Positive Real Lemma/
 * /KYP lemma for continous time QSR dissipative system/

title: LMIs in Control/KYP Lemmas


text:
LMIs in Control/KYP Lemmas/KYP lemma for continous time QSR dissipative system

The System
Consider a contiuous-time LTI system, $$\mathcal{G} : \mathcal{L}_{2e} \rightarrow \mathcal{L}_{2e}$$, with minimal state-space realization (A, B, C, D), where $$\mathcal{A} \in \mathcal{R}^{n\times n}, \mathcal{B} \in \mathcal{R}^{n\times m}, \mathcal{C} \in \mathcal{R}^{p\times n},$$ and $$\mathcal{D} \in \mathcal{R}^{p\times m} $$.

\begin{align} \dot x(t)&=Ax(t)+Bu(t),\\ y(t)&=Cx(t)+Du(t)\\ \end{align}$$

The Data
The matrices $$ A,B,C $$ and $$D $$

The Optimization Problem
The system $$\mathcal{G}$$ is QSR disipative if

 * $$\int_0^T (y^T(t)Qy(t) + 2y^TSu(t) + u^T(t)Ru(t))\,dt \ge 0, \forall u \in \mathcal{L}_{2e}, \forall T \ge 0 $$

where $$u(t)$$ is the input to $$\mathcal{G}, y(t)$$ is the output of $$\mathcal{G}, Q \in \mathcal{S}^{p}, S \in \mathcal{R}^{p\times m},$$ and $$\mathcal{R} \in \mathcal{S}^{m}$$.

LMI : KYP Lemma for QSR Dissipative Systems
The system $$\mathcal{G}$$ is also QSR dissipative if and only if there exists $$ P \in \mathcal{S}^{n},$$ where $$ P > 0,$$ such that

 * $$\begin{bmatrix}

PA + A^{T}P - C^{T}QC & PB - C^{T}S - C^{T}QD \\ (PB - C^{T}S - C^{T}QD)^{T} &  -D^{T}QD - (D^{T}S + S^{T}D) - R \end{bmatrix}\le 0.$$

Conclusion:
If there exist a positive definite $$P$$ for the the selected Q,S and R matrices then the system $$\mathcal{G}$$ is QSR dissipative.

Implementation
Code for implementation of this LMI using MATLAB. https://github.com/VJanand25/LMI


text:
LMIs in Control/Bounded Real Lemma

The System:

\begin{align} \dot x(t)&=Ax(t)+Bu(t)\\ y(t)&=Cx(t)+Du(t) \end{align}$$

The Optimization Problem: Given a state space system of

\begin{align} \dot x(t)&=Ax(t)+Bu(t)\\ y(t)&=Cx(t)+Du(t) \end{align}$$ with A being stable and A$$\in\R^{n*n}$$, B$$\in\R^{n*p}$$,C$$\in\R^{p*n}$$ and D$$\in\R^{p*p}$$ and (A,B,C) being minimal there exists a P=P^T$$\in\R^{n*n}$$ that can be used to solve the bounded real lemma problem using the LMI mentioned below.

The LMI: The Bounded Real Lemma

\begin{align} \begin{bmatrix} A^T P+PA+C^T C&&PB+C^T D\\B^T P+D^T C&& D^T D-I\end{bmatrix}&<0\\ P&>0\\ \end{align}$$ The LMI is feasible if and only if the state space is non expansive. $$\int_{0}^{T} y(t)^T y(t) dt$$<$$\int_{0}^{T} u(t)^T u(t) dt$$ for all solutions of the state space with x(0) = 0, This condition can also be expressed in terms of the transfer matrix H. Nonexpansivity is equivalent to the transfer matrix H satisfying the bounded-real condition, $$H(s)*H(s)<=I$$ for all $$ Re s>0$$

Conclusion:

The LMI is feasible, if and only if the Hamiltonian Matrix M has no imaginary eigenvalues.

Related LMIs:

1. KYP Lemma. https://en.wikibooks.org/wiki/LMIs_in_Control/KYP_Lemmas/KYP_Lemma_(Bounded_Real_Lemma)

Implementation
A link to CodeOcean or other online implementation of the LMI (in progress)

title: LMIs in Control/Bounded Real Lemma


text:
User talk:173.76.246.128

Warning
—Atcovi (Talk - Contribs) 15:30, 14 November 2019 (UTC)

Verification Million
This page has been queried by another Wikibooks user. It does not appear to be part of a book and seems unlikely to be the start of a book. If improvements aren't made, the page may be deleted in 7 days.--ЗAНИA talk 02:25, 5 January 2020 (UTC)

title: User talk:173.76.246.128


text:
User talk:96.5.121.250

Warning
—Atcovi (Talk - Contribs) 15:32, 14 November 2019 (UTC)

title: User talk:96.5.121.250


text:
History of Tennessee

Table of Contents

 * /Introduction/
 * /Indigenous "Tennessee" (to 1800)/
 * /Antebellum Tennessee (1796-1861)/
 * /Civil War, Reconstruction, and the Gilded Age in Tennessee (1861-1900)/
 * /Jim Crow Laws and Customs (1886-1955)/
 * /Modern Tennessee (1901-1941)/
 * /WWII and Post-War Tennessee (1942-present)/
 * /Tennessee in US Popular Culture (1795-present)/
 * /Further Reading/

title: History of Tennessee