A less conservative method for designing H-infinity filters for linear time-delay systems

This paper focuses on H-infinity filtering for linear time-delay systems. A new Lyapunov-Krasovskii functional (LKF) is constructed by uniformly dividing the delay interval into two subintervals, and choosing different Lyapunov matrices on each subinterval. Based on this new LKF, a less conservative delay-dependent bounded real lemma (BRL) is established to ensure that the resulting filtering error system is asymptotically stable with a prescribed H-infinity performance. Then, this new BRL is equivalently converted into a set of linear matrix inequalities, which guarantee the existence of a suitable H-infinity filter. Compared with some existing filtering results, some imposed constraints on the Lyapunov matrices are removed through derivation of the sufficient condition for the existence of the filter. Numerical examples show that the results obtained in this paper significantly improve the H-infinity performance of the filtering error system over some existing results in the literature.