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Periodic solution of the system with impulsive state feedback control

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Abstract

The order-1 periodic solution of the system with impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 periodic solution of the semi-continuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of Poincarè criterion. Finally, we analyze numerically the theoretical results obtained.

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Acknowledgments

We would like to sincerely thank the reviewers for their careful reading of the original manuscript and many valuable comments and suggestions that greatly improved the presentation of this paper. This work is supported by the National Natural Science Foundation of China (11161052, 11371306), the Natural Science Foundation of Guangxi Province (2011jjA10044), the Scientific Research Foundation of Guangxi Education Office (201012MS183) and the Sustentation Fund of the Elitists for Guangxi Universities (GJRC0831).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Yulin Normal University, Yulin, 537000, Guangxi, China

    Guoping Pang & Lansun Chen

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Lansun Chen

Authors
  1. Guoping Pang
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  2. Lansun Chen
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Correspondence to Guoping Pang.

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Pang, G., Chen, L. Periodic solution of the system with impulsive state feedback control. Nonlinear Dyn 78, 743–753 (2014). https://doi.org/10.1007/s11071-014-1473-3

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