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Review of Some Control Theory Results on Uniform Stability of Impulsive Systems

Author

Listed:
  • Bin Liu

    (College of Science, Hunan University of Technology, Zhuzhou 412000, China)

  • Bo Xu

    (College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412000, China)

  • Guohua Zhang

    (College of Science, Hunan University of Technology, Zhuzhou 412000, China)

  • Lisheng Tong

    (College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412000, China)

Abstract

This paper aims to review some uniform stability results for impulsive systems. For the review, we classify the models of impulsive systems into time-based impulsive systems and state-based ones, including continuous-time impulsive systems, discrete-time impulsive systems, stochastic impulsive systems, and impulsive hybrid systems. According to these models, we review, respectively, the related stability concepts and some representative results focused on uniform stability, including the results on uniform asymptotic stability, input-to-state stability (ISS), KLL -stability (uniform stability expressed by KLL -functions), event-stability, and event-ISS. And we formulate some questions for those not fully developed aspects on uniform stability at each subsection.

Suggested Citation

  • Bin Liu & Bo Xu & Guohua Zhang & Lisheng Tong, 2019. "Review of Some Control Theory Results on Uniform Stability of Impulsive Systems," Mathematics, MDPI, vol. 7(12), pages 1-28, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1186-:d:293907
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    References listed on IDEAS

    as
    1. Liu, Bin & Hill, David J. & Sun, Zhijie, 2018. "Input-to-state-KL-stability and criteria for a class of hybrid dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 124-140.
    2. Liu, Bin & Sun, Zhijie & Luo, Yihao & Zhong, Yuxuan, 2019. "Uniform synchronization for chaotic dynamical systems via event-triggered impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    3. E. K. Boukas & H. Yang, 1996. "Stability of stochastic systems with jumps," Mathematical Problems in Engineering, Hindawi, vol. 3, pages 1-13, January.
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    Citations

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    Cited by:

    1. Angelo Alessandri, 2020. "Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    2. Daniel Ríos-Rivera & Alma Y. Alanis & Edgar N. Sanchez, 2020. "Neural-Impulsive Pinning Control for Complex Networks Based on V-Stability," Mathematics, MDPI, vol. 8(9), pages 1-20, August.
    3. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.

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