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The Scientific World Journal
Volume 2013, Article ID 514823, 7 pages
Research Article

Stability Switches of Arbitrary High-Order Consensus in Multiagent Networks with Time Delays

School of Automation, Wuhan University of Technology, Wuhan 430070, China

Received 6 July 2013; Accepted 7 August 2013

Academic Editors: C. W. Ahn, J. Montero, and D. Simson

Copyright © 2013 Bo Yang. 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.


High-order consensus seeking, in which individual high-order dynamic agents share a consistent view of the objectives and the world in a distributed manner, finds its potential broad applications in the field of cooperative control. This paper presents stability switches analysis of arbitrary high-order consensus in multiagent networks with time delays. By employing a frequency domain method, we explicitly derive analytical equations that clarify a rigorous connection between the stability of general high-order consensus and the system parameters such as the network topology, communication time-delays, and feedback gains. Particularly, our results provide a general and a fairly precise notion of how increasing communication time-delay causes the stability switches of consensus. Furthermore, under communication constraints, the stability and robustness problems of consensus algorithms up to third order are discussed in details to illustrate our central results. Numerical examples and simulation results for fourth-order consensus are provided to demonstrate the effectiveness of our theoretical results.