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Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems

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  • Peng, Xiao
  • Wang, Yijing
  • Zuo, Zhiqiang

Abstract

This paper deals with the stabilization problem for non-smooth variable-order Riemann-Liouville fractional switched systems with all modes unstable in the presence of unknown nonlinearity. A controller containing the discontinuous switching item and Riemann-Liouville fractional-order derivative term is firstly designed. By applying fractional order calculation, non-smooth analysis theory and Lyapunov stability theory, some criteria are established under the joint design of controller and state-dependent switching law. An application to variable-order fractional switched permanent magnet synchronous motors is demonstrated and relevant numerical simulations for considered system are given to verify the validity of our designed scheme.

Suggested Citation

  • Peng, Xiao & Wang, Yijing & Zuo, Zhiqiang, 2022. "Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    • Handle: RePEc:eee:apmaco:v:415:y:2022:i:c:s0096300321007827
    DOI: 10.1016/j.amc.2021.126725
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    References listed on IDEAS

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    1. Jiang, Jingfei & Chen, Huatao & Guirao, Juan L.G. & Cao, Dengqing, 2019. "Existence of the solution and stability for a class of variable fractional order differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 269-274.
    2. Ding, Xiuyong & Liu, Xiu, 2017. "On stabilizability of switched positive linear systems under state-dependent switching," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 92-101.
    3. Su, Guangwang & Lu, Liang & Tang, Bo & Liu, Zhenhai, 2020. "Quasilinearization technique for solving nonlinear Riemann-Liouville fractional-order problems," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    4. Heydari, Mohammad Hossein & Avazzadeh, Zakieh & Yang, Yin, 2019. "A computational method for solving variable-order fractional nonlinear diffusion-wave equation," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 235-248.
    5. Wu, Fei & Gao, Renbo & Liu, Jie & Li, Cunbao, 2020. "New fractional variable-order creep model with short memory," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    6. Wang, Yuanqing & Xu, Ning & Liu, Yajuan & Zhao, Xudong, 2021. "Adaptive fault-tolerant control for switched nonlinear systems based on command filter technique," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    7. Yang, Min & Wang, Qiru, 2016. "Approximate controllability of Riemann–Liouville fractional differential inclusions," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 267-281.
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    Cited by:

    1. Cui, Zhe & Sun, Yang & Tian, Wende & Liu, Bin & Guo, Qingjie, 2023. "Dynamic optimal control of coal chemical looping gasification based on process modeling and complex risk computation," Energy, Elsevier, vol. 282(C).

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