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Mathematical Problems in Engineering
Volume 2015, Article ID 138276, 6 pages
Research Article

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

1School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China
2State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 15 September 2015; Revised 21 October 2015; Accepted 22 October 2015

Academic Editor: Peng Lin

Copyright © 2015 Xue Li 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.


We are concerned with the consensus problems for networks of second-order agents, where each agent can only access the relative position information from its neighbours. We aim to find the largest tolerable input delay such that the system consensus can be reached. We introduce a protocol with time-delay and fixed topology. A sufficient and necessary condition is given to guarantee the consensus. By using eigenvector-eigenvalue method and frequency domain method, it is proved that the largest tolerable time-delay is only related to the eigenvalues of the graph Laplacian. And simulation results are also provided to demonstrate the effectiveness of our theoretical results.