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

This paper investigates the problem of robust nonfragile fuzzy H∞ 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∞ 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∞ 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.