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Abstract and Applied Analysis
Volume 2014, Article ID 397532, 14 pages
Research Article

Global μ-Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays

1Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China
2Department of Mathematics, Yangzhou University, Yangzhou 225002, China
3Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Received 10 April 2014; Accepted 5 May 2014; Published 27 May 2014

Academic Editor: Zidong Wang

Copyright © 2014 Xiaofeng 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.


The impulsive complex-valued neural networks with three kinds of time delays including leakage delay, discrete delay, and distributed delay are considered. Based on the homeomorphism mapping principle of complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks is proposed in terms of linear matrix inequality (LMI). By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global -stability of the complex-valued neural networks are established in LMIs. As direct applications of these results, several criteria on the exponential stability, power-stability, and log-stability are obtained. Two examples with simulations are provided to demonstrate the effectiveness of the proposed criteria.