A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay

This paper investigates the problem of delay-dependent robust
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filtering design for a class of uncertain discrete-time state-delayed Takagi-Sugeno (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 fuzzy-basis-dependent Lyapunov-Krasovskii functional combined with Finsler's lemma and an improved free-weighting matrix technique for delay-dependent criteria, a new sufficient condition for robust
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performance analysis is first derived, and then, the filter synthesis is developed. It is shown that by using a simple 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 (LMIs), which are numerically efficient with commercially available software. Finally, simulation examples are provided to illustrate the advantages and less conservatism of the proposed approach.