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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 3567682, 10 pages
http://dx.doi.org/10.1155/2016/3567682
Research Article

Distributed Control for Multiagent Consensus Motions with Nonuniform Time Delays

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

Received 23 February 2016; Accepted 19 May 2016

Academic Editor: Zhan Shu

Copyright © 2016 Mengji Shi and Kaiyu Qin. 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.

Abstract

This paper solves control problems of agents achieving consensus motions in presence of nonuniform time delays by obtaining the maximal tolerable delay value. Two types of consensus motions are considered: the rectilinear motion and the rotational motion. Unlike former results, this paper has remarkably reduced conservativeness of the consensus conditions provided in such form: for each system, if all the nonuniform time delays are bounded by the maximal tolerable delay value which is referred to as “delay margin,” the system will achieve consensus motion; otherwise, if all the delays exceed the delay margin, the system will be unstable. When discussing the system which is intended to achieve rotational consensus motion, an expanded system whose state variables are real numbers (those of the original system are complex numbers) is introduced, and corresponding consensus condition is given also in the form of delay margin. Numerical examples are provided to illustrate the results.