Delay-Induced Consensus and Quasi-Consensus in Multi-Agent Dynamical Systems

Wenwu Yu*, Guanrong Chen, Ming Cao, Wei Ren

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

90 Citations (Scopus)


This paper studies consensus and quasi-consensus in multi-agent dynamical systems. A linear consensus protocol in the second-order dynamics is designed where both the current and delayed position information is utilized. Time delay, in a common perspective, can induce periodic oscillations or even chaos in dynamical systems. However, it is found in this paper that consensus and quasi-consensus in a multi-agent system cannot be reached without the delayed position information under the given protocol while they can be achieved with a relatively small time delay by appropriately choosing the coupling strengths. A necessary and sufficient condition for reaching consensus in multi-agent dynamical systems is established. It is shown that consensus and quasi-consensus can be achieved if and only if the time delay is bounded by some critical value which depends on the coupling strength and the largest eigenvalue of the Laplacian matrix of the network. The motivation for studying quasi-consensus is provided where the potential relationship between the second-order multi-agent system with delayed positive feedback and the first-order system with distributed-delay control input is discussed. Finally, simulation examples are given to illustrate the theoretical analysis.

Original languageEnglish
Pages (from-to)2679-2687
Number of pages9
JournalIEEE Transactions on Circuits and Systems I - Regular papers
Issue number10
Publication statusPublished - Oct-2013


  • Algebraic graph theory
  • delay-induced consensus
  • multi-agent system
  • quasi-consensus

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