LMIs in Control/pages/Discrete Time H∞ Optimal Dynamic Output Feedback Control

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Discrete-Time H∞-Optimal Dynamic Output Feedback Control

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.

A Dynamic Output feedback controller is designed for a Discrete Time system, to minimize the H∞ norm of the closed loop system with exogenous input and performance output .

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:

is minimized while obeying the LMI constraints.

The LMI:[edit | edit source]

Discrete-Time H∞-Optimal Dynamic Output Feedback Control

The LMI formulation

H∞ norm <

The controller is recovered by

and the matrixes and satisfies

Given and , the matrices and can be found using a matrix decomposition, such as a LU decomposition or a Cholesky decomposition.

If , ≠ 0, and ≠ 0, then it is often simplest to choose in order to satisfy the equality constraint

Conclusion:[edit | edit source]

The Discrete-Time H∞-Optimal Dynamic Output Feedback Controller is the system

Implementation[edit | edit source]

A link to CodeOcean or other online implementation of the LMI

Related LMIs[edit | edit source]

[1] - Continuous Time H∞ Optimal Dynamic Output Feedback Control

External Links[edit | edit source]

A list of references documenting and validating the LMI.

Return to Main Page:[edit | edit source]