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Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties

Author

Listed:
  • Chen, Liping
  • Wu, Ranchao
  • He, Yigang
  • Yin, Lisheng

Abstract

Robust stability and stabilization of fractional-order uncertain linear systems with order α:0<α<1 and 1⩽α<2 are considered in the paper. A new polytopic type uncertain state-space model for fractional-order linear systems is addressed, which allows second-order uncertain parameters. The uncertainty in the fractional-order model appears in terms of a polytope of matrices. Some sufficient criteria for the robust asymptotical stable and stabilization for such fractional-order uncertain linear systems are derived. All the results are obtained in terms of linear matrix inequalities (LMIs). Numerical examples are presented to demonstrate the validity and feasibility of the obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:274-284
    DOI: 10.1016/j.amc.2014.12.103
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    References listed on IDEAS

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    1. Xing, Sheng Yan & Lu, Jun Guo, 2009. "Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1163-1169.
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    Cited by:

    1. Liu, Dan & Zhao, Song & Luo, Xiaoyuan & Yuan, Yi, 2021. "Synchronization for fractional-order extended Hindmarsh-Rose neuronal models with magneto-acoustical stimulation input," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Luo, Tianjiao, 2019. "Stabilization of multi-group models with multiple dispersal and stochastic perturbation via feedback control based on discrete-time state observations," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 396-410.
    3. 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.
    4. Kang Xu & Liping Chen & Minwu Wang & António M. Lopes & J. A. Tenreiro Machado & Houzhen Zhai, 2020. "Improved Decentralized Fractional PD Control of Structure Vibrations," Mathematics, MDPI, vol. 8(3), pages 1-13, March.

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