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

< LMIs in Control | pages

**Discrete-Time Lyapunov Stability**

**The System**Edit

Discrete-Time System

**The Data**Edit

The matrices .

**The Optimization Problem**Edit

The following feasibility problem should be solved:

Find P obeying the LMI constraints.

**The LMI:**Edit

Discrete-Time Lyapunov Stability

The LMI formulation

**Conclusion:**Edit

If there exists a satisfying the LMI then, and the equilibrium point of the system is Lyapunov stable.

**Implementation**Edit

- [] - MATLAB implementation of the LMI.

**Related LMIs**Edit

Continuous_Time_Lyapunov_Inequality - Lyapunov_Inequality

## 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.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.