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Robust stabilization of descriptor fractional-order interval systems with uncertain derivative matrices

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  • Di, Ying
  • Zhang, Jin-Xi
  • Zhang, Xuefeng

Abstract

This paper considers the admissibility of descriptor fractional-order interval systems (DFOISs) with order α belonging to (0,2). Firstly, the necessary and sufficient conditions of admissibility for descriptor fractional-order systems (DFOSs) are given in terms of linear matrix inequalities (LMI) which differ from the existing literature. Secondly, for the derivative matrix with interval uncertainties, the criteria of quadratic admissibility for DFOISs are derived by projection lemma. Thirdly, both the state and derivative feedback controllers of DFOISs with interval uncertainties in all matrices are obtained directly without normalization. Finally, three numerical examples are presented to verify the effectiveness of proposed results.

Suggested Citation

  • Di, Ying & Zhang, Jin-Xi & Zhang, Xuefeng, 2023. "Robust stabilization of descriptor fractional-order interval systems with uncertain derivative matrices," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    • Handle: RePEc:eee:apmaco:v:453:y:2023:i:c:s009630032300245x
    DOI: 10.1016/j.amc.2023.128076
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    1. Huang, Lan-Lan & Baleanu, Dumitru & Mo, Zhi-Wen & Wu, Guo-Cheng, 2018. "Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 166-175.
    2. Aghayan, Zahra Sadat & Alfi, Alireza & Mousavi, Yashar & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. Liu, Xiang & Wang, Peiguang & Anderson, Douglas R., 2022. "On stability and feedback control of discrete fractional order singular systems with multiple time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Zhu, Zhen & Lu, Jun-Guo, 2021. "Robust stability and stabilization of hybrid fractional-order multi-dimensional systems with interval uncertainties: An LMI approach," Applied Mathematics and Computation, Elsevier, vol. 401(C).
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    Cited by:

    1. Muhammad Zeeshan Malik & Shiqing Zhang & Guang Chen & Mamdouh L. Alghaythi, 2023. "Robust Tilt-Integral-Derivative Controllers for Fractional-Order Interval Systems," Mathematics, MDPI, vol. 11(12), pages 1-14, June.

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