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Journal of Applied Mathematics
Volume 2013, Article ID 359750, 8 pages
Research Article

Consensus Analysis of Second-Order Multiagent Systems with General Topology and Time Delay

1College of Science, North China University of Technology, Beijing 100144, China
2Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
3School of Electrical and Electronics Engineering, East China Jiaotong University, Nanchang 330013, China
4College of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China
5School of Electric and Information Engineering, Guangxi University of Science and Technology, Liuzhou 545006, China

Received 27 November 2012; Revised 21 February 2013; Accepted 24 February 2013

Academic Editor: Vijay Gupta

Copyright © 2013 Bo Liu 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 addresses the consensus of second-order multiagent systems with general topology and time delay based on the nearest neighbor rule. By using the Laplace transform technique, it is proved that the second-order multi-agent system in the presence of time-delay can reach consensus if the network topology contains a globally reachable node and time delay is bounded. The bound of time-delay only depends on eigenvalues of the Laplacian matrix of the system. The main contribution of this paper is that the accurate state of the consensus center and the upper bound of the communication delay to make the agents reach consensus are given. Some numerical simulations are given to illustrate the theoretical results.