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Stabilisability of discrete-time multi-agent systems under fixed and switching topologies

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  • Yongqiang Guan
  • Xianglei Kong

Abstract

This paper studies the problem of stabilisability for general discrete-time linear multi-agent systems. For fixed topology, a necessary and sufficient graph-theoretic condition is proposed. Based on this, a general linear form of the external control input is given, and two methods to design the feedback gain matrix by Riccati equality/inequality are given. For switching topology, a sufficient graph-theoretic condition is presented, under which the stabilisability of multi-agent systems is achieved by introducing an averaging analysis approach. Additionally, both results under fixed and switching topologies are applied for solving the tracking and formation control of discrete-time multi-agent systems, and some sufficient and/or necessary conditions are presented. Finally, numerical examples are given to illustrate the theoretical results.

Suggested Citation

  • Yongqiang Guan & Xianglei Kong, 2019. "Stabilisability of discrete-time multi-agent systems under fixed and switching topologies," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(2), pages 294-306, January.
    • Handle: RePEc:taf:tsysxx:v:50:y:2019:i:2:p:294-306
    DOI: 10.1080/00207721.2018.1551975
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