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LMIs in Control/pages/L2 gain of Lure systems
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The System
The Data
The matrices .
The Optimization Problem:
The following semi-definite problem should be solved.
Implementation
https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/12a7039f9e3d966e24b43fd58a3cce3725282ed2
Conclusion
The value function returns the square of the smallest provable upper bound on the gain of the Lure's system.
Remark
The Lyapunov function which is used to proof is similar to the one for the systems with unknown parameters.
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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