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A note on the stability of fractional order systems

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  • Tavazoei, Mohammad Saleh
  • Haeri, Mohammad

Abstract

In this paper, a new approach is suggested to investigate stability in a family of fractional order linear time invariant systems with order between 1 and 2. The proposed method relies on finding a linear ordinary system that possesses the same stability property as the fractional order system. In this way, instead of performing the stability analysis on the fractional order systems, the analysis is converted into the domain of ordinary systems which is well established and well understood. As a useful consequence, we have extended two general tests for robust stability check of ordinary systems to fractional order systems.

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  • Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2009. "A note on the stability of fractional order systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1566-1576.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:5:p:1566-1576
    DOI: 10.1016/j.matcom.2008.07.003
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    1. Qiu, Zhiping & Müller, Peter C. & Frommer, Andreas, 2001. "Ellipsoidal set-theoretic approach for stability of linear state-space models with interval uncertainty," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(1), pages 45-59.
    2. N/A, 1970. "Note," Review of Radical Political Economics, Union for Radical Political Economics, vol. 2(4), pages 1-1, October.
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    12. Silva-Juárez, Alejandro & Tlelo-Cuautle, Esteban & de la Fraga, Luis Gerardo & Li, Rui, 2021. "Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    13. W. K. Zahra & S. M. Elkholy, 2012. "The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-16, August.
    14. Dongya Li & Xiaoping Zhang & Shuang Wang & Fengxiang You, 2022. "Robust Synchronization of Fractional-Order Chaotic System Subject to Disturbances," Mathematics, MDPI, vol. 10(24), pages 1-15, December.
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