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Stability for discrete-time uncertain systems with infinite Markov jump and time-delay

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Abstract

In this paper, we developed a stability analysis for discrete-time uncertain time-delay systems governed by an infinite-state Markov chain (DUTSs-IMC). Some sufficient conditions for the considered systems to be exponential stability in mean square with conditioning (ESMS-C) are derived via linear matrix inequalities (LMIs), which can be examined conveniently. Under novel sufficient conditions, the equivalence among asymptotical stability in mean square (ASMS), stochastic stability (SS), exponential stability in mean square (ESMS), and ESMS-C has been established. Besides, numerical simulations are employed in result validation.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61673013, 61733008, 61573156), Natural Science Foundation of Shandong Province (Grant No. ZR2016JL022), and Key Research and Development Plan of Shandong Province (Grant No. 2019GGX101052).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Ting Hou

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qiangdao, 266590, China

    Ting Hou & Yueying Liu

  3. School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510641, China

    Feiqi Deng

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  1. Ting Hou
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  2. Yueying Liu
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  3. Feiqi Deng
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Correspondence to Feiqi Deng.

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Hou, T., Liu, Y. & Deng, F. Stability for discrete-time uncertain systems with infinite Markov jump and time-delay. Sci. China Inf. Sci. 64, 152202 (2021). https://doi.org/10.1007/s11432-019-2897-9

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  • DOI: https://doi.org/10.1007/s11432-019-2897-9

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