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

  • Liguang Xu
  • Wen Liu
  • Hongxiao Hu
  • Weisong ZhouEmail author
Original Paper


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.


Boundedness Fractional-order Intermittent control Lyapunov function 



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.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest in preparing this article.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsZhejiang University of TechnologyHangzhouChina
  2. 2.College of ScienceUniversity of Shanghai for Science and TechnologyShanghaiChina
  3. 3.College of ScienceChongqing University of Posts and TelecommunicationsChongqingChina

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