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Mathematical Problems in Engineering
Volume 2015, Article ID 767456, 16 pages
http://dx.doi.org/10.1155/2015/767456
Research Article

New Delay-Dependent Exponential Stability Criteria for Neural Networks with Mixed Time-Varying Delays

Wu Wen1 and Kaibo Shi2,3

1Department of Academic Affairs Office, Sichuan University of Arts and Science of China, Dazhou 635000, China
2School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
3Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Received 17 December 2014; Revised 8 April 2015; Accepted 15 April 2015

Academic Editor: Asier Ibeas

Copyright © 2015 Wu Wen and Kaibo Shi. 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

This study is concerned with the problem of new delay-dependent exponential stability criteria for neural networks (NNs) with mixed time-varying delays via introducing a novel integral inequality approach. Specifically, first, by taking fully the relationship between the terms in the Leibniz-Newton formula into account, several improved delay-dependent exponential stability criteria are obtained in terms of linear matrix inequalities (LMIs). Second, together with some effective mathematical techniques and a convex optimization approach, less conservative conditions are derived by constructing an appropriate Lyapunov-Krasovskii functional (LKF). Third, the proposed methods include the least numbers of decision variables while keeping the validity of the obtained results. Finally, three numerical examples with simulations are presented to illustrate the validity and advantages of the theoretical results.