Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 247587, 13 pages
doi:10.1155/2010/247587
Research Article

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

Enwen Zhu,1,2,3 Hanjun Zhang,2 and Jiezhong Zou4

1School of Mathematics and Computational Science, Xiangtan University, 411105 Hunan, China
2School of Mathematics and Computational Science, Changsha University of Science and Technology, 410076 Hunan, China
3Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080 Beijing, China
4School of Mathematics, Central South University, 410075 Hunan, China

Received 26 January 2010; Accepted 5 March 2010

Academic Editor: Andrei Volodin

Copyright © 2010 Enwen Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.