LMIs in Control/pages/Discrete-Time Quadratic Stability

From Wikibooks, open books for an open world
Jump to navigation Jump to search

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:

Where .

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]

  • [1] - Matlab implementation using the YALMIP framework and Mosek solver

Related LMIs: =[edit | edit source]

External Links[edit | edit source]

A list of references documenting and validating the LMI.

Return to Main Page:[edit | edit source]