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Consensus seeking over Markovian switching networks with time-varying delays and uncertain topologies

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  • Shang, Yilun

Abstract

Stochastic consensus problems for linear time-invariant multi-agent systems over Markovian switching networks with time-varying delays and topology uncertainties are dealt with. By using the linear matrix inequality method and the stability theory of Markovian jump linear system, we show that consensus can be achieved for appropriate time delays and topology uncertainties which are not caused by the Markov process, provided the union of topologies associated with the positive recurrent states of the Markov process admits a spanning tree and the agent dynamics is stabilizable. Feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time-varying delays. Numerical examples are given to show the feasibility of theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:1234-1245
    DOI: 10.1016/j.amc.2015.08.115
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Zhao, Lin & Yu, Jinpeng & Lin, Chong & Yu, Haisheng, 2017. "Distributed adaptive fixed-time consensus tracking for second-order multi-agent systems using modified terminal sliding mode," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 23-35.
    2. María Jesús García-Ligero & Aurora Hermoso-Carazo & Josefa Linares-Pérez, 2022. "Distributed Fusion Estimation in Network Systems Subject to Random Delays and Deception Attacks," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
    3. Zhao, Lin & Jia, Yingmin & Yu, Jinpeng & Du, Junping, 2017. "H∞ sliding mode based scaled consensus control for linear multi-agent systems with disturbances," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 375-389.
    4. Cheng-Yu Tang & Jun-Ting Lin, 2019. "Bidirectional Power Flow Control of a Multi Input Converter for Energy Storage System," Energies, MDPI, vol. 12(19), pages 1-16, September.
    5. Li, Hongjie & Zhu, Yinglian & jing, Liu & ying, Wang, 2018. "Consensus of second-order delayed nonlinear multi-agent systems via node-based distributed adaptive completely intermittent protocols," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 1-15.
    6. María Jesús García-Ligero & Aurora Hermoso-Carazo & Josefa Linares-Pérez, 2020. "Distributed Fusion Estimation with Sensor Gain Degradation and Markovian Delays," Mathematics, MDPI, vol. 8(11), pages 1-19, November.
    7. Ismi Rosyiana Fitri & Jung-Su Kim, 2020. "A Nonlinear Model Predictive Control with Enlarged Region of Attraction via the Union of Invariant Sets," Mathematics, MDPI, vol. 8(11), pages 1-15, November.

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