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 SystemEdit

Discrete-Time System

 

The DataEdit

The matrices: System  .

The Optimization ProblemEdit

The following feasibility problem should be optimized:

Find P obeying the LMI constraints.

The LMI:Edit

Discrete-Time Bounded Real Lemma

The LMI formulation

 

Conclusion:Edit

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

ImplementationEdit

A link to CodeOcean or other online implementation of the LMI
MATLAB Code

Related LMIsEdit

Continuous_Time_Lyapunov_Inequality - Lyapunov_Inequality

External LinksEdit

A list of references documenting and validating the LMI.


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