Delay-dependent robust H℞ filtering design for uncertain discrete-time T-S fuzzy systems with interval time-varying delay

This paper investigates the problem of delay-dependent robust H
℞
filtering design for a class of uncertain discrete-time state-delayed T-S fuzzy systems. The state delay is assumed to be time-varying and of an interval-like type, which means that both the lower and upper bounds of the time-varying delay are available. The parameter uncertainties are assumed to have a structured linear fractional form. Based on a novel delay and fuzzy-basis-dependent Lyapunov-Krasovskii functional combined with Finsler’s Lemma, a new sufficient condition for robust H
℞
performance analysis is firstly derived and then the filter synthesis is developed. It is shown that by using a new linearization technique incorporating a bounding inequality, a unified framework can be developed such that both the full-order and reduced-order filters can be obtained by solving a set of linear matrix inequalities, which are numerically efficient with commercially available software. Finally, a numerical example is provided to illustrate the advantages and less conservatism of the proposed approach.