Delay-dependent exponential stability for Markovian jumping stochastic Cohen-Grossberg neural networks with p-Laplace diffusion and partially known transition rates via a differential inequality

Ruofeng Rao,Xiongrui Wang,Shouming Zhong

doi:10.1186/1687-1847-2013-183

Abstract

In this paper, new stochastic global exponential stability criteria for delayed impulsive Markovian jumping p-Laplace diffusion Cohen-Grossberg neural networks (CGNNs) with partially unknown transition rates are derived based on a novel Lyapunov-Krasovskii functional approach, a differential inequality lemma and the linear matrix inequality (LMI) technique. The employed methods are different from those of previous related literature to some extent. Moreover, a numerical example is given to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.

Highlights

It is well known that Cohen-Grossberg in [ ] proposed originally the Cohen-Grossberg neural networks (CGNNs)
CGNNs with Markovian jumping parameters have been extensively studied due to the fact that systems with Markovian jumping parameters are useful in modeling abrupt phenomena such as random failures, operating in different points of a nonlinear plant, and changing in the interconnections of subsystems [ – ]
Since stochastic noise disturbance is always unavoidable in practical neural networks, it may be necessary to consider the stability of the null solution of the following Markovian jumping CGNNs:

Summary

Introduction

It is well known that Cohen-Grossberg in [ ] proposed originally the Cohen-Grossberg neural networks (CGNNs). To the best of our knowledge, stochastic stability for the delayed impulsive Markovian jumping p-Laplace diffusion CGNNs has rarely been considered. ). further we only need to consider the stability of the null solution of CohenGrossberg neural networks. Bn(vn(t, x)))T such that there exists a positive definite matrix B = diag(B , B , . Since stochastic noise disturbance is always unavoidable in practical neural networks, it may be necessary to consider the stability of the null solution of the following Markovian jumping CGNNs:. A system with three operation modes may have the transition rate matrix as follows:. The condition |H| = H is not too stringent for a semi-positive definite matrix H = (hij)n×n ≥. Pin) be a positive definite matrix for a given i, and v be a solution of system

Main results

Conclusions