LMIs in Control/pages/Discrete Time Stabilizability

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Discrete-Time Stabilizability

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.

Discrete-Time LTI systems can be made stable using controller gain K, which can be found using LMI optimization, such that the close loop system is stable.

The System[edit | edit source]

Discrete-Time LTI System with state space realization

The Data[edit | edit source]

The matrices: System .

The Optimization Problem[edit | edit source]

The following feasibility problem should be optimized:

Maximize P while obeying the LMI constraints.
Then K is found.

The LMI:[edit | edit source]

Discrete-Time Stabilizability

The LMI formulation

Conclusion:[edit | edit source]

The system is stabilizable iff there exits a , such that . The matrix is Schur with

Implementation[edit | edit source]

A link to CodeOcean or other online implementation of the LMI

Related LMIs[edit | edit source]

[1] - Continuous Time Stabilizability

External Links[edit | edit source]

A list of references documenting and validating the LMI.

Return to Main Page:[edit | edit source]