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Robust stability and stabilization of hybrid fractional-order multi-dimensional systems with interval uncertainties: An LMI approach

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  • Zhu, Zhen
  • Lu, Jun-Guo

Abstract

The hybrid fractional-order multi-dimensional (N-D) systems described by Roesser model are introduced in this paper. The N-D systems include discrete-time dimensions and fractional-order continuous-time dimensions with fractional-order 0<αi<1. Firstly, some novel sufficient stability conditions for nominal hybrid fractional-order N-D systems are presented. Then, against interval uncertainties, the sufficient conditions for robust stability and stabilization of hybrid fractional-order N-D systems are derived. All the results are in the form of linear matrix inequalities. Finally, illustrative examples are given to verify the validity of our results, and demonstrate that our results are less conservative than the existing ones.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:401:y:2021:i:c:s0096300321001235
    DOI: 10.1016/j.amc.2021.126075
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    2. Roxana Motorga & Vlad Mureșan & Mihaela-Ligia Ungureșan & Mihail Abrudean & Honoriu Vălean & Iulia Clitan, 2022. "Artificial Intelligence in Fractional-Order Systems Approximation with High Performances: Application in Modelling of an Isotopic Separation Process," Mathematics, MDPI, vol. 10(9), pages 1-32, April.
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    5. Zhang, Jia-Rui & Lu, Jun-Guo & Zhang, Qing-Hao, 2024. "Robust asymptotic stability analysis for fractional-order systems with commensurate time delays: The 1 < β ≤ 2 case," Applied Mathematics and Computation, Elsevier, vol. 475(C).

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