If topological analysis explains what the system is about, what it consists of/in, what it is, use of.
If it is the purpose of the system, in a broad sense, use for.
In many cases, both would be possible and correct, in which case of is usually preferred. Sometimes one of these prepositions would be incorrect for no apparent reason, even though it should have been possible if you consider its meaning:
- a cup of tea
- ? a cup for tea — [sounds odd: it's just that we're too much used to "tea-cup" in this sense]
Topological-analysis system (you need a hyphen) looks acceptable but a bit less stylistically pleasing than the other two. I'd use such noun adjectives mainly with short words, such as hot-water tap. Because there is no preposition, the reader will have to guess what kind of connection there is between one noun phrase and the other. In addition, he needs to read a large part of the sentence and understand what it is about before he can tell which word belongs to which; consider this example:
The spectrometer robots system analysis utilizes is malfunctioning.
Is it spectrometer robot and system analysis? Or spectrometer robot system and analysis? Or spectrometer and robot system analysis? Compare to this sentence:
The spectrometer analysis of the robots system utilizes is malfunctioning.
This is still a terribly ugly sentence, but at least the reader will see that there is only one possible reading after a few tries. This is just a demonstration of the fact that noun adjectives generally provide less information about the structure of a sentence than other, wordier constructions. (To make this sentence acceptable, add that after spectrometer.)