Discrete-Time Quadratic StabilityEdit
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 matrices .
The Optimization ProblemEdit
The following feasibility problem should be solved:
In case of polytopic uncertainty:
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
-  - Matlab implementation using the YALMIP framework and Mosek solver
Related LMIs: =Edit
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.