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SMC for phase-type stochastic nonlinear semi-Markov jump systems

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Abstract

This paper concerns the issue of sliding mode control (SMC) for phase-type stochastic nonlinear semi-Markov jump systems (S-MJSs) via the T-S fuzzy strategy. One unrealistic assumption, that is, the sojourn time in stochastic switching systems follows an exponential distribution, is removed in this paper by S-MJSs model, which is one of the main features compared to the existing literatures. First, by using the plant transformation method and the supplementary variable technique, phase-type S-MJSs are equivalent to associated Markov jump systems (MJSs). Then, an integral sliding surface function is established to cope with the influence of the switching phenomenon in the plant. By using Lyapunov functions and inequality optimization problems, sufficient conditions are provided for stochastic stability of the system with a prescribed \(H_\infty \) performance index. In addition, a fuzzy SMC law is synthesized to guarantee that the associated T-S fuzzy MJSs fulfill the reaching condition in bounded time. Finally, the validity of the conclusions is verified by the single-link robot arm model.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by National Natural Science Foundation of China under Grant 62073188, Grant 61773235, Grant 61773236, and Grant 61873331, and Natural Science Foundation of Shandong under Grant ZR2019YQ29.

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Authors and Affiliations

  1. School of Engineering, Qufu Normal University, Rizhao, 276826, China

    Meng Gao & Wenhai Qi

  2. School of Automation and Electrical Engineering, Linyi University, Linyi, 276005, China

    Wenhai Qi

  3. School of Mathematics, Southeast University, Nanjing, 211189, China

    Jinde Cao

  4. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, Republic of Korea

    Jinde Cao

  5. College of Mathematics and Statistics, Guangxi Normal University, Guilin, 541006, China

    Jun Cheng

  6. School of Information Science and Engineering, Chengdu University, Chengdu, 610106, China

    Kaibo Shi

  7. College of Information and Control Engineering, Weifang University, Weifang, 261061, China

    Yunteng Gao

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  1. Meng Gao
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Correspondence to Wenhai Qi.

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Gao, M., Qi, W., Cao, J. et al. SMC for phase-type stochastic nonlinear semi-Markov jump systems. Nonlinear Dyn 108, 279–292 (2022). https://doi.org/10.1007/s11071-022-07200-4

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