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Mathematical Problems in Engineering
Volume 2017, Article ID 8965124, 11 pages
https://doi.org/10.1155/2017/8965124
Research Article

Analysis and Design of Adaptive Synchronization of a Complex Dynamical Network with Time-Delayed Nodes and Coupling Delays

1School of Mechanical-Electronic and Automobile Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
2Beijing Key Laboratory of Service Performance of Urban Rail Transit Vehicles, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
3School of Electrical and Information Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China

Correspondence should be addressed to Yu Miao; moc.361@reoaimrevilo

Received 7 April 2017; Revised 28 August 2017; Accepted 19 September 2017; Published 19 October 2017

Academic Editor: Alessandro Lo Schiavo

Copyright © 2017 Yu Miao 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

This paper is devoted to the study of synchronization problems in uncertain dynamical networks with time-delayed nodes and coupling delays. First, a complex dynamical network model with time-delayed nodes and coupling delays is given. Second, for a complex dynamical network with known or unknown but bounded nonlinear couplings, an adaptive controller is designed, which can ensure that the state of a dynamical network asymptotically synchronizes at the individual node state locally or globally in an arbitrary specified network. Then, the Lyapunov-Krasovskii stability theory is employed to estimate the network coupling parameters. The main results provide sufficient conditions for synchronization under local or global circumstances, respectively. Finally, two typical examples are given, using the M-G system as the nodes of the ring dynamical network and second-order nodes in the dynamical network with time-varying communication delays and switching communication topologies, which illustrate the effectiveness of the proposed controller design methods.