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Asymptotic stabilization of general nonlinear fractional-order systems with multiple time delays

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Abstract

In this paper, two new control methods based on a Lyapunov-like function and a vector Lyapunov function separately were put forward to solve the asymptotic stabilization problem of general fractional-order nonlinear systems with multiple time delays. First, we deduced a new asymptotic stabilization control criterion based on a Lyapunov-like function after discussing the asymptotic stability criterion of general fractional-order nonlinear systems. Moreover, to address the problem of multiple time delays of the nonlinear system, we derived another asymptotic stabilization control criterion based on a vector Lyapunov function and an M-matrix via the new controller. Finally, the feasibility and effectiveness of the proposed controllers were verified by several common fractional-order nonlinear systems.

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Acknowledgements

This study was supported in part by the National Nature Science Foundation of China (No. 61573299), the Hunan Provincial Innovation Foundation For Postgraduate (CX20190304).

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  1. College of Electrical and Information Engineering, Hunan University, Changsha, 410082, China

    Zhang Zhe & Zhang Jing

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  1. Zhang Zhe
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  2. Zhang Jing
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Correspondence to Zhang Zhe.

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Zhe, Z., Jing, Z. Asymptotic stabilization of general nonlinear fractional-order systems with multiple time delays. Nonlinear Dyn 102, 605–619 (2020). https://doi.org/10.1007/s11071-020-05866-2

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  • DOI: https://doi.org/10.1007/s11071-020-05866-2

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