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Sliding mode control for nonlinear stochastic systems with Markovian jumping parameters and mode-dependent time-varying delays

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Abstract

This paper reports on the sliding mode control (SMC) problem for nonlinear stochastic systems with one features: time-delays are not only varied with time but also characterized by random delays changed in line with a set of Markov chains (namely, time-delays are mode-dependent time-varying delays). Based on given systems, an integral switching surface is introduced. In particular, such a switching surface with an Itô process is given so that the traditional assumption imposed on systems is removed. And by applying the Itô formula, the linear matrix inequalities method and the lemma provided, more relaxed and indeed delay-dependent criteria for the second moment exponential stability are given. Then, the sliding mode controller is constructed to guarantee the reachability of the switching surface and the existence of the sliding mode. Finally, the validity and the application for the presented SMC method are illustrated by the DC motor system.

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Acknowledgements

This work was partly supported by the National Natural Science Foundation of China (61673257, 11501367, 61573095), and China Postdoctoral Science Foundation (2019M661322).

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Authors and Affiliations

  1. College of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Dongbing Tong & Cong Xu

  2. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, 201620, China

    Qiaoyu Chen

  3. College of Information Sciences and Technology, Donghua University, Shanghai, 200051, China

    Wuneng Zhou

  4. School of Finance, Nanjing Audit University, Jiangsu, 211815, China

    Yuhua Xu

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  1. Dongbing Tong
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  3. Qiaoyu Chen
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Correspondence to Dongbing Tong.

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Tong, D., Xu, C., Chen, Q. et al. Sliding mode control for nonlinear stochastic systems with Markovian jumping parameters and mode-dependent time-varying delays. Nonlinear Dyn 100, 1343–1358 (2020). https://doi.org/10.1007/s11071-020-05597-4

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