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

TL;DR

This paper introduces a novel fuzzy $H_{ olinebreak\infty}$ filter design for nonlinear time-delay systems that allows mismatched premise membership functions, enhancing robustness and reducing conservativeness through new integral inequalities and LMI conditions.

Contribution

It proposes a new fuzzy $H_{ olinebreak\infty}$ filter design method accommodating mismatched membership functions, improving robustness and reducing conservativeness in nonlinear time-delay systems.

Findings

The proposed method outperforms traditional approaches in numerical examples.

The new integral inequality provides tighter bounds, reducing conservativeness.

LMI-based conditions facilitate practical filter design.

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.