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A complete result on the Lyapunov stability of Caputo fractional-order nonautonomous systems by the comparison method

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Abstract

As the other alternative method than the Lyapunov direct method for studying the Lyapunov stability of Caputo fractional-order nonautonomous systems, the comparison method still remains incomplete, due to the lack of a series of fundamental results such as the continuation theorem, the derivation of the Caputo fractional derivatives of Lyapunov functions along trajectories, and the general comparison principle for a long time. Recently, all these prerequisite results have been worked out. Based on them, a complete comparison method (for local and global Lyapunov stability analysis) is established in this paper. It is finally applied to examples with numerical simulation.

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  1. Institutes for Systems Genetics, West China Hospital, Sichuan University, Chengdu, 610041, China

    Cong Wu

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  1. Cong Wu
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Correspondence to Cong Wu.

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Wu, C. A complete result on the Lyapunov stability of Caputo fractional-order nonautonomous systems by the comparison method. Nonlinear Dyn 105, 2473–2483 (2021). https://doi.org/10.1007/s11071-021-06756-x

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