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Mathematical Problems in Engineering
Volume 2015, Article ID 185854, 11 pages
http://dx.doi.org/10.1155/2015/185854
Research Article

LMI-Based Stability Criterion for Impulsive Delays Markovian Jumping Time-Delays Reaction-Diffusion BAM Neural Networks via Gronwall-Bellman-Type Impulsive Integral Inequality

1Department of Mathematics, Chengdu Normal University, Chengdu, Sichuan 611130, China
2Institution of Mathematics, Yibin University, Yibin, Sichuan 644007, China
3School of Science Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China

Received 2 February 2015; Revised 23 June 2015; Accepted 25 June 2015

Academic Editor: Asier Ibeas

Copyright © 2015 Ruofeng Rao 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

Lyapunov stability theory, variational methods, Gronwall-Bellman-type inequalities theorem, and linear matrices inequality (LMI) technique are synthetically employed to obtain the LMI-based global stochastic exponential stability criterion for a class of time-delays Laplace diffusion stochastic equations with large impulsive range under Dirichlet boundary value, whose backgrounds of physics and engineering are the impulsive Markovian jumping time-delays reaction-diffusion BAM neural networks. As far as the authors know, it is the first time to derive the LMI-based criterion by way of Gronwall-Bellman-type inequalities, which can be easily and efficiently computed by computer Matlab LMI toolbox. And the obtained criterion improves the allowable upper bounds of impulse against those of some previous related literature. Moreover, a numerical example is presented to illustrate the effectiveness of the proposed methods.