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Consensus seeking in a network of discrete-time linear agents with communication noises

Author

Listed:
  • Yunpeng Wang
  • Long Cheng
  • Zeng-Guang Hou
  • Min Tan
  • Chao Zhou
  • Ming Wang

Abstract

This paper studies the mean square consensus of discrete-time linear time-invariant multi-agent systems with communication noises. A distributed consensus protocol, which is composed of the agent's own state feedback and the relative states between the agent and its neighbours, is proposed. A time-varying consensus gain a[k] is applied to attenuate the effect of noises which inherits in the inaccurate measurement of relative states with neighbours. A polynomial, namely ‘parameter polynomial’, is constructed. And its coefficients are the parameters in the feedback gain vector of the proposed protocol. It turns out that the parameter polynomial plays an important role in guaranteeing the consensus of linear multi-agent systems. By the proposed protocol, necessary and sufficient conditions for mean square consensus are presented under different topology conditions: (1) if the communication topology graph has a spanning tree and every node in the graph has at least one parent node, then the mean square consensus can be achieved if and only if ∑∞k = 0a[k] = ∞, ∑∞k = 0a2[k]

Suggested Citation

  • Yunpeng Wang & Long Cheng & Zeng-Guang Hou & Min Tan & Chao Zhou & Ming Wang, 2015. "Consensus seeking in a network of discrete-time linear agents with communication noises," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(10), pages 1874-1888, July.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:10:p:1874-1888
    DOI: 10.1080/00207721.2013.837544
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    References listed on IDEAS

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    1. Wu, Zhihai & Peng, Li & Xie, Linbo & Wen, Jiwei, 2013. "Stochastic bounded consensus tracking of leader–follower multi-agent systems with measurement noises based on sampled-data with small sampling delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 918-928.
    2. Peter Wieland & Jung-Su Kim & Frank Allgöwer, 2011. "On topology and dynamics of consensus among linear high-order agents," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(10), pages 1831-1842.
    3. Haibo Jiang & Jianjiang Yu & Caigen Zhou, 2011. "Consensus of multi-agent linear dynamic systems impulsive control protocols," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(6), pages 967-976.
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    Cited by:

    1. 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.

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