A matrix inequality based design method for consensus problems in multi-agent systems

Guisheng Zhai, Shohei Okuno, Joe Imae, Tomoaki Kobayashi

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


In this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.

Original languageEnglish
Pages (from-to)639-646
Number of pages8
JournalInternational Journal of Applied Mathematics and Computer Science
Issue number4
Publication statusPublished - 2009 Dec 1
Externally publishedYes


  • Consensus
  • Decentralized control
  • Graph Laplacian
  • LMI
  • Matrix inequality
  • Multi-agent systems

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Engineering (miscellaneous)
  • Applied Mathematics


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