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Consensus for multi‐agent systems under double integrator dynamics with time‐varying communication delays
Author(s) -
Liu Kaien,
Xie Guangming,
Wang Long
Publication year - 2011
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1792
Subject(s) - upper and lower bounds , double integrator , control theory (sociology) , topology (electrical circuits) , protocol (science) , multi agent system , mathematics , integrator , lyapunov function , linear matrix inequality , computer science , control (management) , mathematical optimization , nonlinear system , mathematical analysis , bandwidth (computing) , medicine , computer network , physics , alternative medicine , pathology , combinatorics , artificial intelligence , quantum mechanics
SUMMARY In this paper, the consensus control problems for multi‐agent systems under double integrator dynamics with time‐varying communication delays are investigated. We assume that the interaction graphs among agents are directed. Two kinds of protocols are considered. One is an absolute damping protocol, and the other is a relative damping protocol. For the first protocol, Lyapunov–Razumikhin functional techniques are used. We derive sufficient conditions that guarantee that all agents asymptotically reach consensus under fixed topology and switching topology, respectively. Moreover, the allowable upper bound for communication delays is given. For the second protocol, Lyapunov–Krasovskii functional techniques are used. Linear matrix inequality (LMI)‐form sufficient conditions are obtained to guarantee the consensus problems to be solved under fixed topology and switching topology, respectively. The allowable upper bound for communication delays is given as well. The feasibilities of the demanded LMIs are also discussed. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.