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Quantization-based tracking control for fuzzy singularly perturbed Markov jump systems with incomplete transition information and packet dropout

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Abstract

In this article, the tracking control problem for discrete-time singularly perturbed systems with a piecewise-homogeneous Markov chain subject to the effect of quantization and packet dropout is addressed based on Takagi–Sugeno (T–S) fuzzy-approximation. Firstly, the stochastic variation of mode transition probabilities with time-varying peculiarities is considered in a finite set, which is dominated by a higher-level homogeneous Markov chain. Moreover, partially unknown information in higher-level transition probabilities (HTPs) matrix is resolved by constructing a unified framework, which covers the stochastic switching and arbitrary switching as special cases, simultaneously. Secondly, considering the burden of network communication between components, the quantization impact and packet dropout caused by network network-induced constraints are integrated into the co-design of fuzzy tracking controller, which is mode-dependent and variation-dependent. Several criteria for the stochastic stability and \({\mathcal {H}}_{\infty }\) performance of the augmented system are deduced by establishing a series of linear matrix inequalities. Ultimately, two simulation examples are given to verify the practicability and effectiveness of the proposed control design schemes.

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Funding

This work was supported in part by the National Natural Science Foundation of China under Grants 11661028, the Natural Science Foundation of Guangxi under Grant 2020GXNSFAA159141, Guangxi Philosophy and Social Science Programming Project (2022) under Grant 22BTJ001.

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Authors and Affiliations

  1. College of Science, Guilin University of Technology, Guilin, 541004, Guangxi, People’s Republic of China

    Fang Guo & Mengzhuo Luo

  2. Guangxi Colleges and Universities Key Laboratory of Applied Statistics, Guilin, 541004, People’s Republic of China

    Mengzhuo Luo

  3. College of Mathematics and Statistics, Guangxi Normal University, Guilin, 541006, Guangxi, People’s Republic of China

    Jun Cheng

  4. School of Cyber Science and Engineering, Sichuan University, Chengdu, 610065, Sichuan, People’s Republic of China

    Xin Wang

  5. School of Information Science and Engineering, Chengdu University, Chengdu, 610106, Sichuan, People’s Republic of China

    Kaibo Shi

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  1. Fang Guo
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Correspondence to Mengzhuo Luo.

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Guo, F., Luo, M., Cheng, J. et al. Quantization-based tracking control for fuzzy singularly perturbed Markov jump systems with incomplete transition information and packet dropout. Nonlinear Dyn 111, 9255–9273 (2023). https://doi.org/10.1007/s11071-023-08309-w

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