Delay-dependent exponential stability results for uncertain stochastic Hopfield neural networks with interval time-varying delays

C Pradeep,R Rakkiyappan,A Vinodkumar

doi:10.1007/s40065-012-0005-6

Abstract

This paper is concerned with stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Both the cases of the time-varying delays which may be dif- ferentiable and may not be differentiable are considered in this paper. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay/interval-dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), by introducing some free-weighting matrices. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.

Highlights

In the past two decades, neural networks have received increasing interest owing to their applications in a variety of areas, such as signal processing, pattern recognition, static image processing, associative memory, and combinatorial optimization [9]
To the best of authors knowledge, so far, very few results on the delay/interval-dependent robust exponential stability analysis for uncertain stochastic neural networks with interval time-varying delays are available in the literature
By using the Lyapunov–Krasovskii functional technique, global robust stability conditions for the considered uncertain stochastic neural networks are given in terms of linear matrix inequality (LMI), which can be calculated by MATLAB LMI control toolbox and introducing some free-weighting matrices

Summary

Introduction

In the past two decades, neural networks have received increasing interest owing to their applications in a variety of areas, such as signal processing, pattern recognition, static image processing, associative memory, and combinatorial optimization [9]. It is of practical importance to study the stochastic effects on the stability property of delayed neural networks, see for example [3,4,5,6,11,16,18,19,23,27,29]. To the best of authors knowledge, so far, very few results on the delay/interval-dependent robust exponential stability analysis for uncertain stochastic neural networks with interval time-varying delays are available in the literature. In this paper a class of uncertain stochastic neural networks with interval time-varying delays is considered. By using the Lyapunov–Krasovskii functional technique, global robust stability conditions for the considered uncertain stochastic neural networks are given in terms of LMIs, which can be calculated by MATLAB LMI control toolbox and introducing some free-weighting matrices. The arguments of a function or a matrix will be omitted in the analysis when no confusion can arise

Problem description and preliminaries

Main results

N1T N2

Conclusion