LMIs in Control/pages/Discrete-Time Quadratic Stability

Discrete-Time Quadratic Stability Stability is an important property, stability analysis is necessary for control theory. For robust control, this criterion is applicable for the uncertain discrete-time linear system. It is based on the Discrete Time Lyapunov Stability. The System The Data The matrices . The Optimization Problem The following feasibility problem should be solved: Where . In case of polytopic uncertainty: Conclusion: This LMI allows us to investigate stability for the robust control problem in the case of polytopic uncertainty and gives on the controller for this case Implementation: - Matlab implementation using the YALMIP framework and Mosek solver Related LMIs: = - Discrete Time Stabilizability Polytopic stability for continuous time case Quadratic polytopic stabilization Discrete Time Lyapunov Stability External Links A list of references documenting and validating the LMI. 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. (3.20.2 page 64) LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd. Return to Main Page: Main Page.