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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 7307834, 12 pages
Research Article

Consensus Conditions for High-Order Multiagent Systems with Nonuniform Delays

School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China

Correspondence should be addressed to Kaiyu Qin

Received 20 May 2016; Revised 8 October 2016; Accepted 16 October 2016; Published 9 April 2017

Academic Editor: Guido Ala

Copyright © 2017 Mengji Shi 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.


Consensus of first-order and second-order multiagent systems has been wildly studied. However, the convergence of high-order (especially the third-order to the sixth-order) state variables is also ubiquitous in various fields. The paper handles consensus problems of high-order multiagent systems in the presence of multiple time delays. Obtained by a novel frequency domain approach which properly resolves the challenges associated with nonuniform time delays, the consensus conditions for the first-order and second-order systems are proven to be nonconservative, and those for the third-order to the sixth-order systems are provided in the form of simple inequalities. The method revealed in this article is applicable to arbitrary-order systems, and the results are less conservative than those based on Lyapunov approaches, because it roots in sufficient and necessary criteria of stabilities. Simulations are carried out to validate the theoretical results.