LMIs in Control/pages/Stability of Lure systems
The System[edit | edit source]
The Data[edit | edit source]
The matrices .
The LMI: The Lure's System's Stability[edit | edit source]
The following feasibility problem should be solved as sufficient condition for the stability of the above Lur'e system.
Implementation[edit | edit source]
Conclusion[edit | edit source]
If the feasibility problem with LMI constraints has solution, then the Lure's system is stable.
Remark[edit | edit source]
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 | edit source]
- 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.