Delay-dependent exponential H ∞ ${H_{\infty}}$ filter for uncertain nonlinear singular time-delay systems through T-S fuzzy model

Yuechao Ma,Menghua Chen

doi:10.1186/s13662-015-0547-y

Yuechao Ma, Menghua Chen

Open Access

https://doi.org/10.1186/s13662-015-0547-y

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Journal: Advances in Difference Equations	Publication Date: Aug 7, 2015
Citations: 4	License type: CC BY 4.0

Affiliation: Yanshan University

Abstract

In this paper, the problem of delay-dependent exponential ${H_{\infty}}$ filter is investigated for uncertain nonlinear singular systems with interval time-varying delay through T-S fuzzy model. A new Lyapunov-Krasovskii functional (LKF) is constructed by considering triple integral and the left and right endpoints of the time-delay to obtain a less conservative condition, which can guarantee that the error system is not only exponentially admissible but also satisfying a prescribed ${H_{\infty}}$ performance. Then, by solving the linear matrix inequalities (LMIs), the filter parameter matrices can be obtained. In the end, some numerical simulations are given to illustrate the effectiveness and the benefits of the methods.

Highlights

Filter design is one of the fundamental problems in various engineering applications, especially in the fields of signal processing and control communities
In [ ], the problem of exponential H∞ filtering was studied for discrete-time switched singular time-delay systems
New results on H∞ filtering for fuzzy systems with interval time-varying delays were obtained in [ ]

Summary

Introduction

Filter design is one of the fundamental problems in various engineering applications, especially in the fields of signal processing and control communities. Exponential H∞ filtering for time-varying delay systems was studied through Markovian approach in [ ]. H∞ filtering for a class of discrete-time singular Markovian jump systems with time-varying delays was designed in [ ]. In [ ], the problem of exponential H∞ filtering was studied for discrete-time switched singular time-delay systems. New results on H∞ filtering for fuzzy systems with interval time-varying delays were obtained in [ ]. To the authors’ knowledge, the problem of delay-dependent exponential H∞ filter for nonlinear singular systems with interval time-varying delay through T-S fuzzy model has rarely been reported. Motivated by the above discussions, the problem of delay-dependent exponential H∞ filter for nonlinear singular systems with interval time-varying delay through T-S fuzzy mode is considered in this paper. Taking into account the lemma (Jensen’s integral inequality), Lemma and Lemma , we get

E T Z E – E T Z E

Conclusion