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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 SystemEdit

Discrete-Time LTI System with state space realization  
 

The DataEdit

The matrices: System  

Controller  

The Optimization ProblemEdit

The following feasibility problem should be optimized:

  is minimized while obeying the LMI constraints.

The LMI:Edit

Discrete-Time H∞-Optimal Dynamic Output Feedback Control

The LMI formulation

H∞ norm <  

 

The controller is recovered by

 

where,  
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

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

ImplementationEdit

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

Related LMIsEdit

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

External LinksEdit

A list of references documenting and validating the LMI.

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