LMIs in Control/Stability Analysis/Stability of Lure's Systems
The System edit
The Data edit
The matrices .
The LMI: The Lure's System's Stability edit
The following feasibility problem should be solved as sufficient condition for the stability of the above Lur'e system.
Implementation edit
https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/9030b507b39f658fb34fef8563ce9130d5dc2baa https://codeocean.com/capsule/0232754/tree
Conclusion edit
If the feasibility problem with LMI constraints has solution, then the Lure's system is stable.
Remark edit
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 .
External Links edit
- 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.