# LMIs in Control/pages/Discrete-Time Quadratic Stability

< LMIs in Control | pages

**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 LinksEdit

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.