Abstract
This article studies the problem of H-infinity filtering for linear discrete-time systems with state delay. Via delay partitioning idea, two new H-infinity, filter design methods are proposed with much less conservatism than most existing results. The improvement lies in constructing two new Lyapunov-Krasovslcii functionals by partitioning the known constant lower bound of delay into several segments equally. Using free-weighting matrix and Jensen inequality methods, two new delay-dependent bound real lemmas (BRLs) are obtained, which depend on both the delay and the partitioning number. Based on the obtained BRLs, new H-infinity filter design approaches are proposed in terms of linear matrix inequalities. The results are immediately extended to multiple time delay case and polytopic uncertain case, respectively. Three numerical examples are presented to illustrate the effectiveness and advantage of the proposed approaches. Copyright (C) 2010 John Wiley & Sons, Ltd.