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LMIs in Control/pages/Discrete-Time Lyapunov Stability
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Discrete-Time Lyapunov Stability
The System
Discrete-Time System
The Data
The matrices .
The Optimization Problem
The following feasibility problem should be solved:
Find P obeying the LMI constraints.
The LMI:
Discrete-Time Lyapunov Stability
The LMI formulation
Conclusion:
If there exists a satisfying the LMI then, and the equilibrium point of the system is Lyapunov stable.
Implementation
[] - MATLAB implementation of the LMI.
Related LMIs
Continuous_Time_Lyapunov_Inequality - Lyapunov_Inequality
External Links
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.
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