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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 437819, 7 pages
Research Article

Consensus of Multiagent Systems with Directed Topology and Communication Time Delay Bases on the Laplace Transform

1College of Science, North China University of Technology, Beijing 100144, China
2Key Laboratory of Beijing for Field-Bus Technology & Automation, North China University of Technology, Beijing 100144, China

Received 6 May 2014; Accepted 18 June 2014; Published 1 July 2014

Academic Editor: Wei Zhang

Copyright © 2014 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 investigates the consensus problem of multiagent systems with directed topologies. Different from the literatures, a new method, the Laplace transform, to study the consensus of multiagent systems with directed topology and communication time delay is proposed. The accurate state of the consensus center and the upper bound of the communication delay to make the agents reach consensus are given. It is proved that all the agents could aggregate and eventually form a cohesive cluster in finite time under certain conditions, and the consensus center is only determined by the initial states and the communication configuration among the agents. Finally, simulations are given to illustrate the theoretical results.