LMIs in Control/pages/Discrete Time Lyapunov Stability

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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]

Discrete-Time System

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.

Return to Main Page:[edit | edit source]