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 System 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 Solve for and that minimize the objective function , subject to Conclusion The optimal Hinf filter is recovered by the state-space matrices and Remark 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 Links A list of references documenting and validating the LMI. LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet. LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes. LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd. Return to Main Page: