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Mathematical Problems in Engineering
Volume 2013, Article ID 762861, 10 pages
Research Article

Impulsive Consensus for Leader-Following Multiagent Systems with Fixed and Switching Topology

1Department of Automation, Wuhan University, Wuhan 430072, China
2College of Automation, Huazhong University of Science and Technology, Wuhan 430074, China

Received 29 March 2013; Accepted 2 June 2013

Academic Editor: Chuandong Li

Copyright © 2013 Zhi-Wei 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 studied the consensus problem of the leader-following multiagent system. It is assumed that the state information of the leader is only available to a subset of followers, while the communication among agents occurs at sampling instant. To achieve leader-following consensus, a class of distributed impulsive control based on sampling information is proposed. By using the stability theory of impulsive systems, algebraic graph theory, and stochastic matrices theory, a necessary and sufficient condition for fixed topology and sufficient condition for switching topology are obtained to guarantee the leader-following consensus of the multiagent system. It is found that leader-following consensus is critically dependent on the sampling period, control gains, and interaction graph. Finally, two numerical examples are given to illustrate the effectiveness of the proposed approach and the correctness of theoretical analysis.