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.
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
Solve for
and
that minimize the objective function
, subject to
The optimal Hinf filter is recovered by the state-space matrices
and
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.
A list of references documenting and validating the LMI.