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Swarm stability for high-order linear time-invariant singular multi-agent systems

Author

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  • Jianxiang Xi
  • Zhicheng Yao
  • Guangbin Liu
  • Yisheng Zhong

Abstract

Swarm-stability and swarm-stabilisation problems for high-order linear time-invariant singular multi-agent systems with directed networks are investigated. First, necessary and sufficient conditions for swarm stability and asymptotic swarm stability are proposed, which are independent of the dimensions of Jordan blocks of the Laplacian matrix of the interaction topology. Then, an approach is given to determine the absolute motion as a whole, and it is shown that the absolute motion is completely determined by initial states if the interaction topology is balanced. Furthermore, an approach is presented to determine gain matrices for asymptotic swarm stabilisation. Moreover, leader-following swarm-stability and swarm-stabilisation problems are investigated. Finally, numerical examples are given to demonstrate theoretical results.

Suggested Citation

  • Jianxiang Xi & Zhicheng Yao & Guangbin Liu & Yisheng Zhong, 2015. "Swarm stability for high-order linear time-invariant singular multi-agent systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(8), pages 1458-1471, June.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:8:p:1458-1471
    DOI: 10.1080/00207721.2013.822610
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