LMIs in Control/pages/Discrete-Time Quadratic Stability
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Discrete-Time Quadratic Stability edit
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
The Data edit
The matrices .
The Optimization Problem edit
The following feasibility problem should be solved:
Where .
In case of polytopic uncertainty:
Conclusion: edit
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
- [1] - Matlab implementation using the YALMIP framework and Mosek solver
Related LMIs: = edit
External Links 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.