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Spectral Criterion for Stability of Mean-Field Stochastic Periodic Systems

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Proceedings of 2020 Chinese Intelligent Systems Conference (CISC 2020)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 706))

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Abstract

This paper addresses the problems of stability and stabilizability for discrete-time mean-field stochastic systems with periodic coefficients. In terms of an orthogonal decomposition of system state, a monodromy operator is introduced for the considered dynamics. Based on the spectral distribution of monodromy operator, operator-spectral criteria are presented for asymptotic stability and weak stability, respectively. Further, by a group of coupled difference linear matrix inequalities (LMIs), Lyapunov-type stability criteria are derived for mean-field stochastic periodic systems. In addition, sufficient conditions are also obtained for both asymptotic stabilizability and regional stabilizability in terms of difference LMIs.

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Acknowledgement

This work was supported by the Natural Science Foundation of Shandong Province (ZR2016FM16), the SDUST Research Fund (No. 2015TDJH105), and Jing-Ying Project of Shandong University of Science and Technology.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Yuechen Cui & Hongji Ma

Authors
  1. Yuechen Cui
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  2. Hongji Ma
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Corresponding author

Correspondence to Hongji Ma .

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Editors and Affiliations

  1. School of Automation Science and Electrical Engineering, Beihang University, Beijing, Beijing, China

    Yingmin Jia

  2. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, Beijing, China

    Weicun Zhang

  3. School of Mechanical Engineering and Automation, Beihang University, Beijing, Beijing, China

    Yongling Fu

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Cui, Y., Ma, H. (2021). Spectral Criterion for Stability of Mean-Field Stochastic Periodic Systems. In: Jia, Y., Zhang, W., Fu, Y. (eds) Proceedings of 2020 Chinese Intelligent Systems Conference. CISC 2020. Lecture Notes in Electrical Engineering, vol 706. Springer, Singapore. https://doi.org/10.1007/978-981-15-8458-9_60

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