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Necessary and sufficient conditions for mean square consensus under Markov switching topologies

Author

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  • Guoying Miao
  • Shengyuan Xu
  • Yun Zou

Abstract

This article deals with the mean square consensus problem for second-order discrete-time multi-agent systems. Both cases of systems with and without time delays in Markov switching topologies are considered. With the introduced control protocols, necessary and sufficient conditions for mean square consensus of second-order multi-agent systems are derived. Under the given control protocols in Markov switching topologies, the second-order multi-agent systems can reach mean square consensus if and only if each union of the graphs corresponding to all the nodes in closed sets has a spanning tree. Finally, a simulation example is provided to illustrate the effectiveness of our theoretical results.

Suggested Citation

  • Guoying Miao & Shengyuan Xu & Yun Zou, 2013. "Necessary and sufficient conditions for mean square consensus under Markov switching topologies," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(1), pages 178-186.
  • Handle: RePEc:taf:tsysxx:v:44:y:2013:i:1:p:178-186
    DOI: 10.1080/00207721.2011.598961
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    Cited by:

    1. Dmitry Vengertsev & Hongkeun Kim & Jin Heon Seo & Hyungbo Shim, 2015. "Consensus of output-coupled high-order linear multi-agent systems under deterministic and Markovian switching networks," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(10), pages 1790-1799, July.
    2. Kun Deng & Dayu Huang, 2015. "Optimal Kullback–Leibler approximation of Markov chains via nuclear norm regularisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 2029-2047, August.
    3. Shang, Yilun, 2016. "Consensus seeking over Markovian switching networks with time-varying delays and uncertain topologies," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1234-1245.
    4. Zhihai Wu & Li Peng & Linbo Xie & Jiwei Wen, 2015. "Stochastic bounded consensus tracking of second-order multi-agent systems with measurement noises based on sampled-data with general sampling delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(3), pages 546-561, February.
    5. Yilun Shang, 2015. "Group consensus of multi-agent systems in directed networks with noises and time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(14), pages 2481-2492, October.

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