LMIs in Control/Controller Synthesis/Discrete Time/State Feedback/Closed-Loop Robust Stability and Controller synthesis of Discrete-Time System with Polytopic Uncertainty
Closed-Loop Robust Stability and Controller synthesis of Discrete-Time System with Polytopic Uncertainty edit
Stability is an important property, stability analysis is necessary for control theory. For robust control, an LMI criterion was developed for the discrete case with closed-loop and open-loop system. The open-loop system is obtained by replacing ..
The System edit
The Data edit
The matrices .
In the case of robust polytopic uncertainty control we have:
The Optimization Problem edit
The following feasibility problem should be solved:
Where , for and
Then our controller
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 SeDuMi 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. (3.19.2 page 63)
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
Return to Main Page: edit
- [6]- Main Page.