LMIs in Control/pages/Discrete-Time Lyapunov Stability
< LMIs in Control | pages
Discrete-Time Lyapunov Stability
The System
editDiscrete-Time System
The Data
editThe matrices .
The Optimization Problem
editThe following feasibility problem should be solved:
Find P obeying the LMI constraints.
The LMI:
editDiscrete-Time Lyapunov Stability
The LMI formulation
Conclusion:
editIf 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
editContinuous_Time_Lyapunov_Inequality - Lyapunov_Inequality
External Links
editA 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.