Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays

Hongyi Li,Bing Chen,Qi Zhou,Shengle Fang

doi:10.1016/j.physleta.2008.01.060

Abstract

This Letter deals with the problem of delay-dependent robust exponential stability in mean square for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-varying delays. Based on Lyapunov–Krasovskii functional and the stochastic stability theory, delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Because of introducing some free-weighting matrices to develop the stability criteria, the proposed stability conditions have less conservatism. Numerical examples are given to illustrate the effectiveness of our results.

Highlights

Over last decades, the study of Hopfield neural networks has received considerable attention since they play an important role in various fields such as signal processing, image processing, pattern recognition and optimization problems [1]
The stability analysis for Hopfield neural networks with time-delay has attracted a large amount of research interest and many sufficient conditions have been proposed to guarantee the stability of neural networks with various type of time delays, see for example [2,3,4,5,6,7,8,9,10,11,12,13,14,15], and the references therein
Li et al / Physics Letters A 372 (2008) 3385–3394 knowledge, so far, no result on the delay-dependent robust exponential stability analysis for uncertain stochastic neural networks with discrete and distributed time-varying delays is available in the literature

Summary

Introduction

The study of Hopfield neural networks has received considerable attention since they play an important role in various fields such as signal processing, image processing, pattern recognition and optimization problems [1]. In [24], the problem of stochastic robust stability of uncertain stochastic Hopfield neural networks with time-varying delays was investigated. By introducing slack matrices, delay-dependent robust stability criteria for uncertain stochastic neural networks with time-varying delay were obtained in [25,26]. Some results on stability of stochastic neural networks with finite distributed delay have been presented in [28,29,30]. H. Li et al / Physics Letters A 372 (2008) 3385–3394 knowledge, so far, no result on the delay-dependent robust exponential stability analysis for uncertain stochastic neural networks with discrete and distributed time-varying delays is available in the literature. Motivated by the above observation, in this Letter, we investigate the problem of delay-dependent robust exponential stability for a class of uncertain stochastic neural networks with discrete and distributed time-varying delays. If not explicitly stated, are assumed to have compatible dimensions

Problem formulation

New stability results

Numerical examples

Conclusion