LMIs in Control/pages/Discrete Time Lyapunov Stability
Discrete-Time Lyapunov Stability
A discrete time system operates on a discrete time signal input and produces a discrete time signal output. They are used in digital signal processing, such as digital filters for images or sound. The class of discrete time systems that are both linear and time invariant, known as discrete time LTI systems.
Stability of DT LTI systems can be determined by solving Lyapunov Inequality.
The System[edit | edit source]
The Data[edit | edit source]
The matrices: System .
The Optimization Problem[edit | edit source]
The following feasibility problem should be optimized:
Find P obeying the LMI constraints.
The LMI:[edit | edit source]
Discrete-Time Bounded Real Lemma
The LMI formulation
Conclusion:[edit | edit source]
If there exists a satisfying the LMI then, and the equilibrium point of the system is Lyapunov stable.
Implementation[edit | edit source]
A link to CodeOcean or other online implementation of the LMI
Related LMIs[edit | edit source]
Continuous_Time_Lyapunov_Inequality - Lyapunov_Inequality
External Links[edit | edit source]
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.