LMIs in Control/pages/Discrete Time H2 Optimal Dynamic Output Feedback Control

Discrete-Time H2-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 H2 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  


The Optimization ProblemEdit

The following feasibility problem should be optimized:

  is minimized while obeying the LMI constraints.

The LMI:Edit

Discrete-Time H2-Optimal Full-State Feedback Control

The LMI formulation

H2 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


The Discrete-Time H2-Optimal Dynamic Output feedback controller is the system  


A link to CodeOcean or other online implementation of the LMI

Related LMIsEdit

[1] - Continuous Time H2 Optimal Dynamic Output Feedback Control

External LinksEdit

A list of references documenting and validating the LMI.

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