Brief paper: Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems

  • Authors:

  • Wenwu Yu;Guanrong Chen;Ming Cao

  • Affiliations:

  • Department of Electronic Engineering, City University of Hong Kong, Hong Kong and Department of Mathematics, Southeast University, Nanjing 210096, China;Department of Electronic Engineering, City University of Hong Kong, Hong Kong;Faculty of Mathematics and Natural Sciences, ITM, University of Groningen, The Netherlands

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2010

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Abstract

This paper studies some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. First, basic theoretical analysis is carried out for the case where for each agent the second-order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant. A necessary and sufficient condition is given to ensure second-order consensus and it is found that both the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network play key roles in reaching consensus. Based on this result, a second-order consensus algorithm is derived for the multi-agent system facing communication delays. A necessary and sufficient condition is provided, which shows that consensus can be achieved in a multi-agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value. Finally, simulation examples are given to verify the theoretical analysis.