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LMIs in Control/pages/L2 gain of systems with multiplicative noise
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The System
where , are independent, identically distributed random variables with
and is independent of the process .
The Data
The matrices .
The LMI:
Implementation
https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/a34713575cd8ae9831cb5b7eb759d0fd45a8c37f
Conclusion
The optimal returns an upper bound on the gain of the system. .
Remark
It is straightforward to apply scaling method [Boyd, sec.6.3.4] to obtain component-wise results.
External Links
LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
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