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Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems

Author

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  • Xi, Jianxiang
  • Shi, Zongying
  • Zhong, Yisheng

Abstract

Admissible consensus analysis and consensualizing controller design problems for high-order linear time-invariant singular swarm systems are investigated. Firstly, by projecting the state of a singular swarm system onto a consensus subspace and a complement consensus subspace, a necessary and sufficient condition for admissible consensus is presented in terms of linear matrix inequalities (LMIs). An approach to decrease the calculation complexity is proposed, by which only three LMIs independent of the number of agents need to be checked. Then, by using the changing variable method, sufficient conditions for admissible consensualization are shown. An explicit expression of the consensus function is given, and it is shown that the modes of the consensus function can be arbitrarily placed if each agent is R-controllable and impulse controllable and the interaction topology has a spanning tree. Finally, theoretical results are applied to deal with cooperative control problems of multi-agent supporting systems.

Suggested Citation

  • Xi, Jianxiang & Shi, Zongying & Zhong, Yisheng, 2012. "Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5839-5849.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:5839-5849
    DOI: 10.1016/j.physa.2012.07.008
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    References listed on IDEAS

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    1. Xi, Jianxiang & Cai, Ning & Zhong, Yisheng, 2010. "Consensus problems for high-order linear time-invariant swarm systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5619-5627.
    2. Lin, Peng & Jia, Yingmin, 2008. "Average consensus in networks of multi-agents with both switching topology and coupling time-delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 303-313.
    3. Xi, Jianxiang & Shi, Zongying & Zhong, Yisheng, 2011. "Consensus analysis and design for high-order linear swarm systems with time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4114-4123.
    4. Czirók, András & Vicsek, Tamás, 2000. "Collective behavior of interacting self-propelled particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 17-29.
    5. Peng, Ke & Yang, Yupu, 2009. "Leader-following consensus problem with a varying-velocity leader and time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 193-208.
    6. Hu, Jiangping & Hong, Yiguang, 2007. "Leader-following coordination of multi-agent systems with coupling time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 853-863.
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    Cited by:

    1. repec:eee:phsmap:v:487:y:2017:i:c:p:58-73 is not listed on IDEAS
    2. Pei, Yongquan & Sun, Jitao, 2016. "Consensus analysis of switching multi-agent systems with fixed topology and time-delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 437-444.

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