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Abstract and Applied Analysis
Volume 2013, Article ID 590894, 6 pages
Research Article

On the General Consensus Protocol in Multiagent Networks with Double-Integrator Dynamics and Coupling Time Delay

1College of Software and Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China

Received 24 October 2012; Revised 6 January 2013; Accepted 25 January 2013

Academic Editor: Sheng-Jie Li

Copyright © 2013 Tao Dong and Xiaofeng Liao. 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 considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results.