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Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback

Author

Listed:
  • Jiang Wu

    (School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China)

  • Hao Xie

    (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China)

  • Tianyi Li

    (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China)

  • Wenjian He

    (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China)

  • Tiancan Xi

    (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China)

  • Xiaoling Liang

    (Maritime Engineering College, Dalian Maritime University, No.1 Linghai Road, Dalian 116026, China)

Abstract

This paper focuses on a class of fractional-order systems with state delays and studies the design problem of the finite-time bounded tracking controller. The error system method in preview control theory is first used. By taking fractional-order derivatives of the state equations and error signals, a fractional-order error system is constructed. This transforms the tracking problem of the original system into an input–output finite=time stability problem of the error system. Based on the output equation of the original system and the error signal, an output equation for the error system is constructed, and a memory-based output feedback controller is designed by means of this equation. Using the input–output finite-time stability theory and linear matrix inequality (LMI) techniques, the output feedback gain matrix of the error system is derived by constructing a fractional-order Lyapunov–Krasovskii function. Then, a fractional-order integral of the input to the error system is performed to derive a finite-time bounded tracking controller for the original system. Finally, numerical simulations demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Jiang Wu & Hao Xie & Tianyi Li & Wenjian He & Tiancan Xi & Xiaoling Liang, 2025. "Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback," Mathematics, MDPI, vol. 13(2), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:200-:d:1563575
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    References listed on IDEAS

    as
    1. Wang, Shaojie & He, Shaobo & Yousefpour, Amin & Jahanshahi, Hadi & Repnik, Robert & Perc, Matjaž, 2020. "Chaos and complexity in a fractional-order financial system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Fucheng Liao & Yingxue Wu & Xiao Yu & Jiamei Deng, 2018. "Finite-Time Bounded Tracking Control for Linear Discrete-Time Systems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-10, June.
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