Finite Frequency H-infinity Filtering for Discrete-Time Uncertain Systems

Abstract : This paper is concerned with the problem of finite frequency (FF) H-infinity filter design for linear time-invariant discrete-time systems with polytopic uncertainties. Our aim is to design a new filter guaranteeing an H-infinity performance bound in a FF ranges. The H-infinity filter in designed to deal with noises in Low Frequency (LF) domain. By utilizing the Generalized Kalman-Yakubovich-Popov (GKYP) lemma, projection lemma, and we introduce many slack matrices, the conditions on the existence of H-infinity filters for LF range is unified in terms of solving a set of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to show the effectiveness of the proposed method in comparison with the existing methods.