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Exponential ultimate boundedness of fractional-order differential systems via periodically intermittent control

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Abstract

This article investigates the exponential ultimate boundedness of fractional-order differential systems via periodically intermittent control. By utilizing the Lyapunov function method and the monotonicity of the Mittag-Leffler function along with the periodically intermittent controller, several sufficient conditions ensuring the exponential ultimate boundedness of the addressed systems are obtained. An example is given to explain the obtained results.

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Acknowledgements

The work is supported by the National Natural Science Foundation of China under Grants 11501518, 11771397 and 11701060 and the Natural Science Foundation of Chongqing under Grant KJ1704099. The authors are very grateful to the Editors and the Reviewers for their insightful and constructive comments.

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Authors and Affiliations

  1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310023, China

    Liguang Xu & Wen Liu

  2. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Hongxiao Hu

  3. College of Science, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Weisong Zhou

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  1. Liguang Xu
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  2. Wen Liu
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  3. Hongxiao Hu
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  4. Weisong Zhou
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Correspondence to Weisong Zhou.

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Xu, L., Liu, W., Hu, H. et al. Exponential ultimate boundedness of fractional-order differential systems via periodically intermittent control. Nonlinear Dyn 96, 1665–1675 (2019). https://doi.org/10.1007/s11071-019-04877-y

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  • DOI: https://doi.org/10.1007/s11071-019-04877-y

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