LMIs in Control/pages/H2Optimalfilter

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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. Optimal filters normally are free from stability problems. There are simple operational checks on an optimal filter when it is being used that indicate whether it is operating correctly. Optimal filters are probably easier to make adaptive to parameter changes than suboptimal filters.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.

To ensure that has a finite norm, it is required that , which results in

The LMI: - Optimal filter[edit]

Solve for , and that minimize subject to .


Conclusion:[edit]

The filter is recovered by and .

Implementation[edit]

MATLAB code of Optimal filter

External links[edit]