Robust Nonfragile H∞ Filtering for Uncertain T-S Fuzzy Systems with Interval Delay: A New Delay Partitioning Approach

Abstract

This paper investigates the problem of robust nonfragile fuzzy $H_{\mathrm{\infty }}$ filtering for uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Attention is focused on the design of a filter such that the filtering error system preserves a prescribed $H_{\mathrm{\infty }}$ performance, where the filter to be designed is assumed to have gain perturbations. By developing a delay decomposition approach, both lower and upper bound information of the delayed plant states can be taken into full consideration; the proposed delay-fractional-dependent stability condition for the filter error systems is obtained based on the direct Lyapunov method allied with an appropriate and variable Lyapunov-Krasovskii functional choice and with tighter upper bound of some integral terms in the derivation process. Then, a new robust nonfragile fuzzy $H_{\mathrm{\infty }}$ filter scheme is proposed, and a sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities (LMIs). Finally, some numerical examples are utilized to demonstrate the effectiveness and reduced conservatism of the proposed approach.