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New integral inequalities and asymptotic stability of fractional-order systems with unbounded time delay

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Abstract

The stability analysis of fractional-order systems with unbounded delay remains an open problem. In this paper, we firstly explore two new integral inequalities. Using these two integral inequalities obtained, the Halanay inequality with unbounded delay is extended to Caputo fractional-order case and Riemann–Liouville fractional-order case. Finally, several examples are presented to illustrate the effectiveness and applicability of the fractional Halanay inequalities in obtaining the asymptotic stability conditions of fractional-order systems with unbounded delay.

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Acknowledgements

This work is partially supported by the Fundamental Research Funds for the Central Universities (No. CUSF-DH-D-2017083).

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Authors and Affiliations

  1. College of Information Science and Technology, Donghua University, Shanghai, 201620, People’s Republic of China

    Bin-Bin He

  2. School of Mathematics and Statistics, Central South University, Changsha, 410075, People’s Republic of China

    Hua-Cheng Zhou

  3. Department of Applied Mathematics, Donghua University, Shanghai, 201620, People’s Republic of China

    Chun-Hai Kou

  4. Mechatronics, Embedded Systems and Automation Lab, University of California, Merced, CA, 95343, USA

    YangQuan Chen

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  1. Bin-Bin He
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  2. Hua-Cheng Zhou
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  3. Chun-Hai Kou
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Correspondence to Hua-Cheng Zhou.

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He, BB., Zhou, HC., Kou, CH. et al. New integral inequalities and asymptotic stability of fractional-order systems with unbounded time delay. Nonlinear Dyn 94, 1523–1534 (2018). https://doi.org/10.1007/s11071-018-4439-z

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  • DOI: https://doi.org/10.1007/s11071-018-4439-z

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