Abstract
In this paper, the asymptotic stability problem for Riemann–Liouville fractional-order systems with time delays is investigated. First, a new Lyapunov theorem for asymptotic stability is proved. Then, based on the Lyapunov theorem and fractional-order Jensen inequalities, two delay-dependent and order-dependent conditions for asymptotic stability of Riemann–Liouville fractional-order systems are derived by constructing new classes of Lyapunov functions. The derived criteria are described in terms of linear matrix inequalities, which are computationally efficient. Finally, an example is provided to demonstrate the effectiveness and less conservativeness of the proposed results.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grants 62073217 and 61374030.
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X-CJ, conceptualization, methodology, and writing—original draft. J-GL, supervision and writing—review and editing. Q-HZ, writing—review and editing.
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Xiao-Chuang, J., Jun-Guo, L. & Qing-Hao, Z. Delay-dependent and order-dependent asymptotic stability conditions for Riemann–Liouville fractional-order systems with time delays. Comp. Appl. Math. 42, 116 (2023). https://doi.org/10.1007/s40314-023-02257-2
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DOI: https://doi.org/10.1007/s40314-023-02257-2
Keywords
- Fractional-order system
- Time-delay system
- Fractional-order integral inequality
- Riemann–Liouville fractional-order derivative