A New Fuzzy $H_{\infty}$ Filter Design for Nonlinear Time-Delay Systems with Mismatched Premise Membership Functions

Abstract: This paper is concerned with the fuzzy $H_{\infty}$ filter design issue for nonlinear systems with time-varying delay. To overcome the shortcomings of the conventional methods with matched preconditions, the fuzzy $H_{\infty}$ filter to be designed and the T-S fuzzy model are assumed to have different premise membership functions and number of rules, thus, greater design flexibility and robustness to uncertainty can be achieved. However, such design will also make the derived results conservative, to relax the result, a novel integral inequality which is tighter than the traditional inequalities derived from the Leibniz-Newton formula is applied, besides, a fuzzy Lypunov function and the information of the membership functions are also introduced. All the design methods are presented in LMI-based conditions. Finally, two numerical examples are given to prove the effectiveness and superiority of the proposed approach.