LMIs in Control/pages/Discrete-Time Quadratic Stability

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 SystemEdit

 


The DataEdit

The matrices  .


The Optimization ProblemEdit

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 LinksEdit

A list of references documenting and validating the LMI.


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