411 REFERENCE · Wikibooks
LMIs in Control/Stability Analysis/Stability of Lure's Systems
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
The System
The Data
The matrices .
The LMI: The Lure's System's Stability
The following feasibility problem should be solved as sufficient condition for the stability of the above Lur'e system.
Implementation
https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/9030b507b39f658fb34fef8563ce9130d5dc2baa
https://codeocean.com/capsule/0232754/tree
Conclusion
If the feasibility problem with LMI constraints has solution, then the Lure's system is stable.
Remark
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
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.
Return to Main Page: