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Chin. Phys. B, 2013, Vol. 22(4): 040203    DOI: 10.1088/1674-1056/22/4/040203
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Consensus problems of first-order dynamic multi-agent systems with multiple time delays

Ji Liang-Hao (纪良浩)a b, Liao Xiao-Feng (廖晓峰)a
a State Key Laboratory of Power Transmission Equipment & System Security and New Technology, College of Computer Science, Chongqing University,Chongqing 400044, China;
b College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Abstract  Consensus problems of first-order multi-agent systems with multiple time delays are investigated in this paper. We discuss three cases: 1) continuous, 2) discrete, and 3) a continuous system with a proportional plus derivative controller. In each case, the system contains communication and input time delays simultaneously. Supposing a dynamic multi-agent system with directed topology that contains a globally reachable node, the sufficient convergence condition of the system is discussed with respect to each of the three cases based on the generalized Nyquist criterion and the frequency-domain analysis approach, yielding conclusions that are either less conservative than or in agreement with previously published results. And we know that the convergence condition of the system depends mainly on each agent's input time delay and the adjacent weights but is independent of the communication delay between agents, whether the system is continuous or discrete. Finally, simulation examples are given to verify the theoretical analysis.
Keywords:  multi-agent      time delays      consensus      first-order      convergence  
Received:  27 June 2012      Revised:  22 August 2012      Accepted manuscript online: 
PACS:  02.30.Ks (Delay and functional equations)  
  02.30.Yy (Control theory)  
  05.65.+b (Self-organized systems)  
Fund: Project supported in part by the National Natural Science Foundation of China (Grant Nos. 60973114 and 61170249), in part by the Natural Science Foundation of CQCSTC, (Grant Nos. 2009BA2024 and cstc2011jjA1320), and in part by the State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University (Grant No. 2007DA10512711206).
Corresponding Authors:  Ji Liang-Hao     E-mail:

Cite this article: 

Ji Liang-Hao (纪良浩), Liao Xiao-Feng (廖晓峰) Consensus problems of first-order dynamic multi-agent systems with multiple time delays 2013 Chin. Phys. B 22 040203

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