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Mittag–Leffler stability of nabla discrete fractional-order dynamic systems

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Abstract

In the present study, the definition of discrete Mittag–Leffler stability is derived to characterize convergence rule of the pseudostates for nabla discrete fractional-order dynamic systems. Applying the Lyapunov stability theory, some new criteria are proposed to determine asymptotic stability of the zero equilibrium. In addition, by applying fractional comparison principle, the results are extended from Caputo discrete fractional-order systems to Riemann–Liouville systems. Moreover, a useful inequality is proposed to further improve the availability of the presented methods. Finally, some meticulously designed simulations are provided to verify the correctness and practicability of the elaborated stability notions.

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Acknowledgements

The work described in this paper was supported by the National Natural Science Foundation of China (61573332, 61601431, 61973291) and the fund of China Scholarship Council (201806345002).

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Authors and Affiliations

  1. Department of Automation, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China

    Yingdong Wei, Yiheng Wei, Yuquan Chen & Yong Wang

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  1. Yingdong Wei
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  2. Yiheng Wei
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  3. Yuquan Chen
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  4. Yong Wang
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Correspondence to Yingdong Wei.

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Wei, Y., Wei, Y., Chen, Y. et al. Mittag–Leffler stability of nabla discrete fractional-order dynamic systems. Nonlinear Dyn 101, 407–417 (2020). https://doi.org/10.1007/s11071-020-05776-3

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