Finite frequency approaches to H∞ filtering for continuous-time state-delayed systems

This paper is concerned with the problem of H∞ filter design for linear continuous-time state-delayed systems with finite frequency specifications. The developed approaches in the paper are to design a filter guaranteeing an H∞ performance bound in a finite frequency range for delayed systems. To reduce conservatism, delay-partitioning idea is exploited to derive a new finite frequency bounded real lemma (BRL). By utilizing the generalized Kalman-Yakubovich-Popov lemma and projection lemma, the conditions on the existence of H∞ filters for different finite frequency ranges are unified in terms of solving a set of linear matrix inequalities.