LMIs in Control/pages/Discrete-Time Quadratic Stability
Discrete-Time Quadratic Stability[edit | edit source]
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[edit | edit source]
The Data[edit | edit source]
The matrices .
The Optimization Problem[edit | edit source]
The following feasibility problem should be solved:
In case of polytopic uncertainty:
Conclusion:[edit | edit source]
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:[edit | edit source]
-  - Matlab implementation using the YALMIP framework and Mosek solver
Related LMIs: =[edit | edit source]
- - Discrete Time Stabilizability
- Polytopic stability for continuous time case
- Quadratic polytopic stabilization
- Discrete Time Lyapunov Stability
External Links[edit | edit source]
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.