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Abstract and Applied Analysis
Volume 2013, Article ID 825307, 8 pages
Research Article

Distributed Impulsive Consensus of the Multiagent System without Velocity Measurement

1School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China
2College of Automation, Huazhong University of Science and Technology, Wuhan 430074, China

Received 12 April 2013; Revised 27 June 2013; Accepted 27 June 2013

Academic Editor: Zidong Wang

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 deals with the distributed consensus of the multiagent system. In particular, we consider the case where the velocity (second state) is unmeasurable and the communication among agents occurs at sampling instants. Based on the impulsive control theory, we propose an impulsive consensus algorithm that extends some of our previous work to account for the lack of velocity measurement. By using the stability theory of the impulsive system, some necessary and sufficient conditions are obtained to ensure the consensus of the controlled multiagent system. It is shown that the control gains, the sampled period and the eigenvalues of Laplacian matrix of communication graph play key roles in achieving consensus. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed algorithm.