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LMIs in Control/Controller Synthesis/Continuous Time/Optimal Dynamic Output Feedback/H-infinity

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Discrete-Time H∞-Optimal Dynamic Output Feedback Control

In this section, a Dynamic Output feedback controller is designed for a Continuous Time system, to minimize the H norm of the closed loop system with exogenous input and performance output .

The System

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Continuous-Time LTI System with state space realization

The Data

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The matrices: System

Controller

The Optimization Problem

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The following feasibility problem should be optimized:

is minimized while obeying the LMI constraints.

The LMI:

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Solve for that minimize subject to

where The controller is recovered by


where,
and the matrices and satisfy . If , then and .

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

Conclusion:

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

Implementation

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The LMI given above can be implemented and solved using a tool such as YALMIP, along with an LMI solver such as MOSEK.

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Discrete Time H∞ Optimal Dynamic Output Feedback Control

Continuous Time H2 Optimal Dynamic Feedback Control

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A list of references documenting and validating the LMI.

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