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Research Papers

Impulsive Consensus of Networked Multi-Agent Systems With Distributed Delays in Agent Dynamics and Impulsive Protocols

[+] Author and Article Information
Xinzhi Liu

Department of Applied Mathematics,
University of Waterloo,
Waterloo, ON N2 L 3G1, Canada
e-mail: xinzhi.liu@uwaterloo.ca

Kexue Zhang

Department of Applied Mathematics,
University of Waterloo,
Waterloo, ON N2 L 3G1, Canada
e-mail: kexue.zhang@uwaterloo.ca

Wei-Chau Xie

Department of Civil and
Environmental Engineering,
University of Waterloo,
Waterloo, ON N2 L 3G1, Canada
e-mail: xie@uwaterloo.ca

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received March 22, 2017; final manuscript received August 12, 2018; published online September 21, 2018. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 141(1), 011008 (Sep 21, 2018) (8 pages) Paper No: DS-17-1162; doi: 10.1115/1.4041202 History: Received March 22, 2017; Revised August 12, 2018

This paper studies the consensus problem of networked multi-agent systems (NMASs). Distributed delays are considered in the agent dynamics, and we propose a new type of impulsive consensus protocols that also takes into account of distributed delays. A novel method is developed to estimate the relation between the agent states at the impulsive instants and the distributed-delayed agent states, which helps to use the Razumikhin-type stability result to investigate the consensus of NMASs with distributed-delayed impulses. Sufficient conditions are established to guarantee that the network consensus can be reached via the proposed consensus protocols with fixed and switching topologies, respectively. Numerical simulations are also provided to demonstrate our theoretical results.

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Figures

Grahic Jump Location
Fig. 1

Network topologies with four agents

Grahic Jump Location
Fig. 2

Consensus processes: (a) impulsive consensus with digraph G1; (b) impulsive consensus with digraph G2; (c) impulsive consensus with switching between digraphs G1 and G2; and (d) state trajectories of the error states ei,j(i=1,2,3,4andj=1,2)

Grahic Jump Location
Fig. 3

Periodic switching signal ω(k) for k∈ℕ

Grahic Jump Location
Fig. 4

Illustration of function ζ(t) for t∈[tk−d,tk) and relations between time tk−d and different impulsive instants

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