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Stability of Fractional Order Systems

Author

Listed:
  • Margarita Rivero
  • Sergei V. Rogosin
  • José A. Tenreiro Machado
  • Juan J. Trujillo

Abstract

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

Suggested Citation

  • Margarita Rivero & Sergei V. Rogosin & José A. Tenreiro Machado & Juan J. Trujillo, 2013. "Stability of Fractional Order Systems," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-14, May.
    • Handle: RePEc:hin:jnlmpe:356215
    DOI: 10.1155/2013/356215
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    Cited by:

    1. Rahimabadi, Arsalan & Benali, Habib, 2023. "Extended fractional-polynomial generalizations of diffusion and Fisher–KPP equations on directed networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Fiuzy, Mohammad & Shamaghdari, Saeed, 2023. "Robust H∞-PID control Stability of fractional-order linear systems with Polytopic and two-norm bounded uncertainties subject to input saturation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 550-581.
    3. Dehui Liu & Tianzeng Li & Yu Wang, 2022. "Adaptive Dual Synchronization of Fractional-Order Chaotic System with Uncertain Parameters," Mathematics, MDPI, vol. 10(3), pages 1-16, January.
    4. Oana Brandibur & Roberto Garrappa & Eva Kaslik, 2021. "Stability of Systems of Fractional-Order Differential Equations with Caputo Derivatives," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    5. Marzieh Asadi & Arash Farnam & Hamed Nazifi & Sam Roozbehani & Guillaume Crevecoeur, 2022. "Robust Stability Analysis of Unstable Second Order Plus Time-Delay (SOPTD) Plant by Fractional-Order Proportional Integral (FOPI) Controllers," Mathematics, MDPI, vol. 10(4), pages 1-10, February.
    6. Orest Lozynskyy & Damian Mazur & Yaroslav Marushchak & Bogdan Kwiatkowski & Andriy Lozynskyy & Tadeusz Kwater & Bohdan Kopchak & Przemysław Hawro & Lidiia Kasha & Robert Pękala & Robert Ziemba & Bogus, 2021. "Formation of Characteristic Polynomials on the Basis of Fractional Powers j of Dynamic Systems and Stability Problems of Such Systems," Energies, MDPI, vol. 14(21), pages 1-35, November.

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