LMIs in Control/pages/H2-Optimal Filter

H2-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 There are two methods of synthesizing the H2-optimal filter. Synthesis 1 Solve for and that minimize the objective function , subject to Synthesis 2 Synthesis 2 is identical to Synthesis 1, with the exception of the final two matrix inequality constraints: Remark In both cases, if and then it is often simplest to choose in order to satisfy the equality constraint (above). Conclusion In both cases, the optimal H2 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 methods presented in this page take 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: