LMIs in Control/pages/Hinf-Optimal Filter

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 SystemEdit

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 SynthesisEdit

Solve for  and   that minimize the objective function  , subject to

 

 

 

ConclusionEdit

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

RemarkEdit

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.

External LinksEdit

A list of references documenting and validating the LMI.

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