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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 236782, 22 pages
Research Article

Enhancement of the Quality and Robustness in Synchronization of Nonlinear Lur'e Dynamical Networks

1China Electric Power Research Institute, Beijing 100192, China
2The State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Technology, College of Engineering, Peking University, Beijing 100871, China

Received 28 June 2011; Accepted 9 September 2011

Academic Editor: Zidong Wang

Copyright © 2012 Shiyun Xu 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.


In order to improve the synchronous reliability and dependability of complex dynamical networks, methods need to be proposed to enhance the quality and robustness of the synchronization scheme. The present study focuses on the robust fault detection issue within the synchronization for a class of nonlinear dynamical networks composed by identical Lur'e systems. Sufficient conditions in terms of linear matrix inequalities (LMIs) are established to guarantee global robust synchronization of the network. Under such a synchronization scheme, the error dynamical system is globally asymptotically stable, the effect of external disturbances is suppressed, and at the same time, the network is sensitive to possible faults based on a mixed performance. The fault sensitivity index, moreover, can be optimized via a convex optimization algorithm. The effectiveness and applicability of the analytical results are demonstrated through a network example composed by the Chua's circuit, and it shows that the quality and robustness of synchronization has been greatly enhanced.