LMIs in Control/pages/HInf Optimal Filter

Optimal filtering is a means of adaptive extraction of a weak desired signal in the presence of noise and interfering signals. The goal of optimal filtering is to design a filter that acts on the output of the generalized plant and optimizes the transfer matrix from w to the filtered output.

The System:

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Consider the continuous-time generalized LTI plant with minimal states-space realization

 

where it is assumed that   is Hurwitz.

The Data

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The matrices needed as inputs are  .

The Optimization Problem:

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An  -optimal filter is designed to minimize the   norm of   in following equation.

 


The LMI: - Optimal filter

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Solve for  ,   and   that minimize   subject to  .

 


Conclusion:

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The filter is recovered by   and  .

Implementation

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