Improved Fuzzy $H_{\infty}$ Filter Design Method for Nonlinear Systems with Time-Varing Delay

TL;DR

This paper presents a less conservative fuzzy $H_{ olinebreak} ext{infinity}$ filter design method for nonlinear systems with time-varying delays, utilizing a novel integral inequality and membership function information to improve stability analysis.

Contribution

It introduces a new delay-dependent fuzzy $H_{ olinebreak} ext{infinity}$ filter design approach using LMIs and a novel integral inequality, enhancing existing methods.

Findings

The proposed method achieves better stability margins.

Simulation confirms the effectiveness of the designed filter.

The approach outperforms traditional methods in handling delays.

Abstract

This paper investigates the fuzzy $H_{\infty}$ filter design issue for nonlinear systems with time-varying delay. In order to obtain less conservative fuzzy $H_{\infty}$ filter design method, a novel integral inequality is employed to replace the conventional Lebniz-Newton formula to analyze the stability conditions of the filtering error system. Besides, the information of the membership functions is introduced in the criterion to further relax the derived results. The proposed delay dependent filter design method is presented as LMI-based conditions, and corresponding definite expressions of fuzzy $H_{\infty}$ filter are given as well. Finally, a simulation example is provided to prove the effectiveness and superiority of the designed fuzzy $H_{\infty}$ filter.