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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 638496, 10 pages
http://dx.doi.org/10.1155/2013/638496
Research Article

Asymptotic Stability and Exponential Stability of Impulsive Delayed Hopfield Neural Networks

1Department of Mathematics, Shandong University, Jinan 250100, China
2School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China
3Research Center on Logistics Optimization and Prediction of Engineering Technology, Jinan, Shandong 250014, China
4School of Computer Science, Fudan University, Shanghai 200433, China

Received 27 June 2013; Accepted 11 August 2013

Academic Editor: Jinde Cao

Copyright © 2013 Jing Chen 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

A criterion for the uniform asymptotic stability of the equilibrium point of impulsive delayed Hopfield neural networks is presented by using Lyapunov functions and linear matrix inequality approach. The criterion is a less restrictive version of a recent result. By means of constructing the extended impulsive Halanay inequality, we also analyze the exponential stability of impulsive delayed Hopfield neural networks. Some new sufficient conditions ensuring exponential stability of the equilibrium point of impulsive delayed Hopfield neural networks are obtained. An example showing the effectiveness of the present criterion is given.