2024 Volume 14 Issue 1
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Xia Zhou, Meixuan Xi, Wanbing Liu, Zhongjun Ma, Jinde Cao. DELAYED CONSENSUS IN MEAN-SQUARE OF MASS UNDER MARKOV SWITCHING TOPOLOGIES AND BROWN NOISE[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 543-559. doi: 10.11948/20230307
Citation: Xia Zhou, Meixuan Xi, Wanbing Liu, Zhongjun Ma, Jinde Cao. DELAYED CONSENSUS IN MEAN-SQUARE OF MASS UNDER MARKOV SWITCHING TOPOLOGIES AND BROWN NOISE[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 543-559. doi: 10.11948/20230307
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DELAYED CONSENSUS IN MEAN-SQUARE OF MASS UNDER MARKOV SWITCHING TOPOLOGIES AND BROWN NOISE

  • 1.

    School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China

  • 2.

    Center for Applied Mathematics of Guangxi (Guilin University of Electronic Technology), Guilin 541002, China

  • 3.

    School of Mathematics, Southeast University, Nanjing 210096, China

  • 4.

    Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea

    Abstract

  • The delayed consensus in mean-square issue of nonlinear multi-agent systems (NMASs) under uncertain nonhomogeneous Markov switching (UNMS) topologies and Brown noise is investigated in this paper. Firstly, there are two delays $ d(t) $ and $ \tau $. $ d(t) $ represents the time-varying delay among followers. $ \tau $ stands for the delay between the leader and the followers, which is the delay in delayed consensus in mean-square. When $ \tau=0 $, the delayed consensus degenerates to identical consensus. Secondly, the random communication topologies are modeled as nonhomogeneous Markov switching topologies in which the transition rates (TRs) are partially or totally unknown. Further, communication noise is also considered, which is assumed to be Brown noise. Sufficient conditions of delayed consensus in mean-square for the systems are gained on account of qualitative and stability theory, theory of random differetntial equations and distributed control theory. Finally, the correctness of the results is verified through the example given.

    MSC: 93A16, 93D50
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