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Delay-Dependent and Order-Dependent Guaranteed Cost Control for Uncertain Fractional-Order Delayed Linear Systems

Author

Listed:
  • Fei Qi

    (School of Automation, Chongqing University, Chongqing 400044, China)

  • Yi Chai

    (School of Automation, Chongqing University, Chongqing 400044, China)

  • Liping Chen

    (School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China)

  • José A. Tenreiro Machado

    (Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal)

Abstract

This paper addresses the guaranteed cost control problem of a class of uncertain fractional-order (FO) delayed linear systems with norm-bounded time-varying parametric uncertainty. The study is focused on the design of state feedback controllers with delay such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Stemming from the linear matrix inequality (LMI) approach and the FO Razumikhin theorem, a delay- and order-dependent design method is proposed with guaranteed closed-loop stability and cost for admissible uncertainties. Examples illustrate the effectiveness of the proposed method.

Suggested Citation

  • Fei Qi & Yi Chai & Liping Chen & José A. Tenreiro Machado, 2020. "Delay-Dependent and Order-Dependent Guaranteed Cost Control for Uncertain Fractional-Order Delayed Linear Systems," Mathematics, MDPI, vol. 9(1), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:41-:d:468913
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    References listed on IDEAS

    as
    1. Chen, Liping & Wu, Ranchao & He, Yigang & Yin, Lisheng, 2015. "Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 274-284.
    2. Liang, Song & Wu, Ranchao & Chen, Liping, 2016. "Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 49-62.
    3. Chen, Boshan & Chen, Jiejie, 2015. "Razumikhin-type stability theorems for functional fractional-order differential systems and applications," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 63-69.
    4. Liping Chen & Tingting Li & YangQuan Chen & Ranchao Wu & Suoliang Ge, 2019. "Robust passivity and feedback passification of a class of uncertain fractional-order linear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(6), pages 1149-1162, April.
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    Cited by:

    1. Jiae Yang & Yujia Wang & Tong Wang & Xuebo Yang, 2022. "Fuzzy-Based Tracking Control for a Class of Fractional-Order Systems with Time Delays," Mathematics, MDPI, vol. 10(11), pages 1-22, May.

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