Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 191546, 12 pages
doi:10.1155/2010/191546
Research Article

Stability Analysis of Recurrent Neural Networks with Random Delay and Markovian Switching

Enwen Zhu,1,2 Yong Wang,3 Yueheng Wang,1 Hanjun Zhang,2 and Jiezhong Zou4

1School of Mathematics and Computational Science, Changsha University of Science and Technology, 410076 Hunan, China
2School of Mathematics and Computational Science, Xiangtan University, 411105 Hunan, China
3Department of Mathematics, Harbin Institute of Technology, 150001 Heilongjiang, China
4School of Mathematics, Central South University, 410075 Hunan, China

Received 14 March 2010; Accepted 18 May 2010

Academic Editor: Alexander I. Domoshnitsky

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

In this paper, the exponential stability analysis problem is considered for a class of recurrent neural networks (RNNs) with random delay and Markovian switching. 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 recurrent neural network with Markovian switching is exponentially stable. The analysis is based on the Lyapunov-Krasovskii functional and stochastic analysis approach, and the conditions are expressed in terms of linear matrix inequalities, 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.