Necessary and sufficient conditions for consensus in third order multi-agent systems

Chi Huang, Guisheng Zhai, Gesheng Xu

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


We deal with a consensus control problem for a group of third order agents which are networked by digraphs. Assuming that the control input of each agent is constructed based on weighted difference between its states and those of its neighbor agents, we aim to propose an algorithm on computing the weighting coefficients in the control input. The problem is reduced to designing Hurwitz polynomials with real or complex coefficients. We show that by using Hurwitz polynomials with complex coefficients, a necessary and sufficient condition can be obtained for designing the consensus algorithm. Since the condition is both necessary and sufficient, we provide a kind of parametrization for all the weighting coefficients achieving consensus. Moreover, the condition is a natural extension to second order consensus, and is reasonable and practical due to its comparatively decreased computation burden. The result is also extended to the case where communication delay exists in the control input.

Original languageEnglish
Article number8436488
Pages (from-to)1044-1053
Number of pages10
JournalIEEE/CAA Journal of Automatica Sinica
Issue number6
Publication statusPublished - 2018 Nov


  • Communication delay
  • Hurwitz polynomials
  • consensus algorithms
  • graph Laplacians
  • third order multi-agent systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Information Systems
  • Artificial Intelligence


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