Robust Stability Analysis for T-S Fuzzy Neural Networks with Time-varying Delays

Pin-Lin Liu

doi:10.13189/ujca.2014.020105

Abstract

In this paper, the robust stability of T-S fuzzy uncertain system for neural networks with time-varying delays is investigated. The constraint on the time-varying delay function is removed, which means that a fast time-varying delay is allowed. Based on the Lyapunov- Krasovskii functional techniques and integral inequality approach (IIA), novel robust stability criteria have been derived in terms of linear matrix inequalities which can be easily solved using the efficient convex optimization algorithm. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov-Krasovskii functional. Examples are included to illustrate our results. These results are shown to be less conservative than those reported in the literature.

Highlights

There has been a large amount of literature that studies the stability properties of linear time delay systems
The existing results always assume that the time-varying delay function is continuously differentiable and its derivative is smaller than one, see [7] for example, which is a rigorous constraint
The problem of stability analysis and control synthesis for systems in T-S fuzzy model with time delay have been studied extensively and lot of research works have been reported in the literature [3, 4, 7,8,9,10,11, 15, 16]

Summary

Introduction

There has been a large amount of literature that studies the stability properties of linear time delay systems. The problem of stability analysis and control synthesis for systems in T-S fuzzy model with time delay have been studied extensively and lot of research works have been reported in the literature [3, 4, 7,8,9,10,11, 15, 16]. The integral inequality approach (IIA) [12, 13] has recently been devised to study the stability of time-delay systems, and less conservative stability criteria have been derived. We discuss the stability problem for T-S fuzzy uncertain system for neural networks with time-varying delays by employing an integral inequality approach (IIA). Numerical examples are given to demonstrate the effectiveness and merits of the proposed method

Stability Description and Preliminaries

Main Results

E E T i ci ci

Illustrative Examples

Conclusion