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Abstract and Applied Analysis
Volume 2014, Article ID 453149, 11 pages
Research Article

Generalized Mutual Synchronization between Two Controlled Interdependent Networks

1Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China
2School of Mechanical Engineering and Automation, Xihua University, Chengdu 610039, China

Received 13 January 2014; Accepted 6 February 2014; Published 11 March 2014

Academic Editor: Zhengguang Wu

Copyright © 2014 Quan 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.


This paper mainly focuses on the generalized mutual synchronization between two controlled interdependent networks. First, we propose the general model of controlled interdependent networks and with time-varying internetwork delays coupling. Then, by constructing Lyapunov functions and utilizing adaptive control technique, some sufficient conditions are established to ensure that the mutual synchronization errors between the state variables of networks and can asymptotically converge to zero. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results and to explore potential application in future smart grid. The simulation results also show how interdependent topologies and internetwork coupling delays influence the mutual synchronizability, which help to design interdependent networks with optimal mutual synchronizability.