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Robust passivity and feedback passification of a class of uncertain fractional-order linear systems

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  • Liping Chen
  • Tingting Li
  • YangQuan Chen
  • Ranchao Wu
  • Suoliang Ge

Abstract

Theoretical results on robust passivity and feedback passification of a class of uncertain fractional-order (FO) linear systems are presented in the paper. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output matrices. Firstly, some suitable notions of passivity and dissipativity for FO systems are proposed, and the relationship between passivity and stability is obtained. Then, a sufficient condition in the form of linear matrix inequality (LMI) for such system to be robustly passive is given. Based on this condition, the design method of state feedback controller is proposed when the states are available. Moreover, by using matrix singular value decomposition and LMI techniques, the existing condition and method of designing a robust observer-based passive controller for such systems are derived. Numerical simulations demonstrate the effectiveness of the theoretical formulation.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tsysxx:v:50:y:2019:i:6:p:1149-1162
    DOI: 10.1080/00207721.2019.1597940
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    Cited by:

    1. Padmaja, N. & Balasubramaniam, P., 2022. "Mixed H∞/passivity based stability analysis of fractional-order gene regulatory networks with variable delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 167-181.
    2. Sweetha, S. & Sakthivel, R. & Harshavarthini, S., 2021. "Finite-time synchronization of nonlinear fractional chaotic systems with stochastic actuator faults," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Manuel De la Sen, 2019. "On the Design of Hyperstable Feedback Controllers for a Class of Parameterized Nonlinearities. Two Application Examples for Controlling Epidemic Models," IJERPH, MDPI, vol. 16(15), pages 1-23, July.
    4. 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.
    5. Manuel De la Sen, 2022. "Asymptotic Hyperstability and Input–Output Energy Positivity of a Single-Input Single-Output System Which Incorporates a Memoryless Non-Linear Device in the Feed-Forward Loop," Mathematics, MDPI, vol. 10(12), pages 1-20, June.

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