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Abstract and Applied Analysis
Volume 2013, Article ID 576290, 8 pages
Research Article

Consensus for Multiagent Systems with Heterogeneous Time-Varying Delays

School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China

Received 5 June 2013; Revised 25 October 2013; Accepted 27 October 2013

Academic Editor: Sakthivel Rathinasamy

Copyright © 2013 Beibei Wang and Yuangong Sun. 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 apply the linear matrix inequality method to consensus and consensus problems of the single integrator multiagent system with heterogeneous delays in directed networks. To overcome the difficulty caused by heterogeneous time-varying delays, we rewrite the multiagent system into a partially reduced-order system and an integral system. As a result, a particular Lyapunov function is constructed to derive sufficient conditions for consensus of multiagent systems with fixed (switched) topologies. We also apply this method to the consensus of multiagent systems with disturbances and heterogeneous delays. Numerical examples are given to illustrate the theoretical results.