Asymptotical Mean Square Stability of Cohen-Grossberg Neural Networks with Random Delay

Enwen Zhu,Hanjun Zhang,Jiezhong Zou

doi:10.1155/2010/247587

Abstract

The asymptotical mean-square stability analysis problem is considered for a class of Cohen-Grossberg neural networks (CGNNs) with random delay. The evolution of the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed Cohen-Grossberg neural network is asymptotical mean-square stability. By employing Lyapunov-Krasovskii functionals and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria for the asymptotical mean-square stability, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.

Highlights

It has been widely known that many biological and artificial neural networks contain an inherent time delay, which may cause oscillation and instability see, e.g., 1
The existence of equilibrium point, global asymptotic stability, global exponential stability, and the existence of periodic solutions Journal of Inequalities and Applications have been intensively investigated in recent publications on the broad topics of time-delay systems see, e.g., 2–26
Motivated by the above discussions, the aim of this paper is to investigate the stability of CGNNs with random delay in mean square

Summary

Introduction

It has been widely known that many biological and artificial neural networks contain an inherent time delay, which may cause oscillation and instability see, e.g., 1. In a PULN, the output signal of the node is transferred to another node by multibranches with arbitrary time delay which is random and its probabilistic characteristic can often be measured by the statistical methods For this case, if some values of the time delay are very large but the probabilities of the delay taking such large values are very small, it may result in a more conservative result if only the information of variation range of the time delay is considered. To the best of the authors’ knowledge, so far, the stability analysis of CGNNs with random delay modeled by a continuous-time homogeneous Markov process with a finite number of states has received little attention in the literature. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria

Notations

Problem Formulation

Main Results and Proofs

A Numerical Example

Conclusions