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Consensus problems for high-order linear time-invariant swarm systems

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  • Xi, Jianxiang
  • Cai, Ning
  • Zhong, Yisheng

Abstract

Consensus problems for high-order continuous-time linear time-invariant swarm systems with directed interaction topologies are investigated. A new method to deal with consensus problems is proposed based on state space decomposition. Two subspaces of a complex space are introduced, namely a consensus subspace and a complement consensus subspace. Based on this decomposition, necessary and sufficient conditions for consensus and consensualizability are presented respectively. An approach for determining and designing the consensus function which may be time-varying is shown. The applications of theoretical results in multi-agent supporting systems are studied.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:24:p:5619-5627
    DOI: 10.1016/j.physa.2010.08.038
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    4. 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.
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    Cited by:

    1. 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.
    2. Xi, Jianxiang & Yao, Zhicheng & Wang, Zhong & Liu, Guangbin & Zhong, Yisheng, 2014. "Admissible L2 consensus for singular time-delayed swarm systems with external disturbances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 165-176.
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    6. 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.

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