LMIs in Control/pages/HinfinityOptimalfilter

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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:[edit]

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

where it is assumed that is Hurwitz.

The Data[edit]

The matrices needed as inputs are .

The Optimization Problem:[edit]

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


The LMI: - Optimal filter[edit]

Solve for , and that minimize subject to .


Conclusion:[edit]

The filter is recovered by and .

Implementation[edit]

External links[edit]