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LMIs in Control/pages/Hinf-Optimal Filter

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Hinf-Optimal Filter

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 to the filtered output.

The System

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Consider the continuous-time generalized LTI plant, with minimal state-space representation

where it is assumed that is Hurwitz. A continuous-time dynamic LTI filter with state-space representation

is designed to optimize the transfer function from to , which is given by

where

Optimal Filtering seeks to minimize the given norm of the transfer function

Filter Synthesis

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Solve for and that minimize the objective function , subject to

Conclusion

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The optimal Hinf filter is recovered by the state-space matrices and

Remark

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The problem of optimal filtering can alternatively be formulated as a special case of synthesizing a dynamic output "feedback" controller for the generalized plant given by

The synthesis method presented in this page takes advantage of the fact that the controller in this case is not a true feedback controller, as it only appears as a feedthrough term in the performance channel.

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A list of references documenting and validating the LMI.

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