Abstract and Applied Analysis
Volume 2013 (2013), Article ID 625372, 14 pages
http://dx.doi.org/10.1155/2013/625372
Research Article

Synchronization of General Complex Networks with Hybrid Couplings and Unknown Perturbations

Xinsong Yang,1 Shuang Ai,1 Tingting Su,1 and Ancheng Chang2

1Department of Mathematics, Chongqing Normal University, Chongqing 400047, China
2Department of Mathematics, Hunan Information Science Vocational College, Changsha, Hunan 410151, China

Received 4 January 2013; Accepted 2 February 2013

Academic Editor: Chuangxia Huang

Copyright © 2013 Xinsong Yang 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

The issue of synchronization for a class of hybrid coupled complex networks with mixed delays (discrete delays and distributed delays) and unknown nonstochastic external perturbations is studied. The perturbations do not disappear even after all the dynamical nodes have reached synchronization. To overcome the bad effects of such perturbations, a simple but all-powerful robust adaptive controller is designed to synchronize the complex networks even without knowing a priori the functions and bounds of the perturbations. Based on Lyapunov stability theory, integral inequality Barbalat lemma, and Schur Complement lemma, rigorous proofs are given for synchronization of the complex networks. Numerical simulations verify the effectiveness of the new robust adaptive controller.