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LMIs in Control/Click here to continue/LMIs in system and stability Theory/Output Energy Bound for Lure's Systems
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The System
The Data
The matrices .
The Optimization Problem:
The following optimization problem should be to find the tightest upper bound for the output energy of the above Lur'e system.
Implementation
https://github.com/mkhajenejad/Mohammad-Khajenejad/blob/master/LMIs%20for%20Output%20Energy%20Bounds%20of%20Lure's%20Systems
Conclusion
The value function returns the the lowest bound for the energy function of the Lure's systems, i.e., with initial conditions .
Remark
The key step in the proof is to satisfy , where
is Lyapunov function in a special form.
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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