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Recent progress in impulsive control systems

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  • Yang, Xueyan
  • Peng, Dongxue
  • Lv, Xiaoxiao
  • Li, Xiaodi

Abstract

This paper overviews the research investigations pertaining to impulsive control systems (ICSs). We focus on the fundamental results and recent progress of ICSs. After reviewing the relative literature, this paper will provide a comprehensive and intuitive overview of ICSs. Six aspects of ICSs are surveyed including basic theory, Lyapunov stability, delayed ICSs, input-to-state stability (ISS), finite-time control, and state-dependent impulses. Based on this, the paper provides a reference for further research on ICSs.

Suggested Citation

  • Yang, Xueyan & Peng, Dongxue & Lv, Xiaoxiao & Li, Xiaodi, 2019. "Recent progress in impulsive control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 244-268.
    • Handle: RePEc:eee:matcom:v:155:y:2019:i:c:p:244-268
    DOI: 10.1016/j.matcom.2018.05.003
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    References listed on IDEAS

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    1. Peng Li & Xiaodi Li & Jinde Cao, 2018. "Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative," Complexity, Hindawi, vol. 2018, pages 1-8, January.
    2. 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.
    3. Marão, José & Liu, Xinzhi & Figueiredo, Annibal, 2012. "Using impulses to control the convergence toward invariant surfaces of continuous dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1067-1079.
    4. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    5. Quanxin Zhu & Fubao Xi & Xiaodi Li, 2012. "Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 154-174, July.
    6. Wenjun Xiong & Dan Zhang & Jinde Cao, 2017. "Impulsive synchronisation of singular hybrid coupled networks with time-varying nonlinear perturbation," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(2), pages 417-424, January.
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    Cited by:

    1. Gani Stamov & Ivanka Stamova & George Venkov & Trayan Stamov & Cvetelina Spirova, 2020. "Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations," Mathematics, MDPI, vol. 8(7), pages 1-18, July.
    2. Stamova, Ivanka & Stamov, Trayan & Stamov, Gani, 2022. "Lipschitz stability analysis of fractional-order impulsive delayed reaction-diffusion neural network models," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Gani Stamov & Stefania Tomasiello & Ivanka Stamova & Cvetelina Spirova, 2019. "Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms," Mathematics, MDPI, vol. 8(1), pages 1-20, December.
    4. Wang, Yaqi & Lu, Jianquan & Cao, Jinde & Huang, Wei & Guo, Jianhua & Wei, Yun, 2020. "Input-to-state stability of the road transport system via cyber–physical optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 3-12.
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    7. He, Zhilong & Li, Chuandong & Li, Hongfei & Zhang, Qiangqiang, 2020. "Global exponential stability of high-order Hopfield neural networks with state-dependent impulses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    8. Gonzalo Armienta [y otros] & Eric Tremolada Álvarez (editor) Author-Email, 2020. "Conjuntos geopolíticos, regionalización y procesos de integración en el siglo XXI," Books, Universidad Externado de Colombia, Facultad de Derecho, number 1215.
    9. Wu, Shuchen & Sun, Xiaohui & Li, Xiaodi & Wang, Haipeng, 2020. "On controllability and observability of impulsive control systems with delayed impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 65-78.
    10. Gani Stamov & Ivanka Stamova, 2021. "Impulsive Fractional Differential Inclusions and Almost Periodic Waves," Mathematics, MDPI, vol. 9(12), pages 1-15, June.
    11. Gani Stamov & Ivanka Stamova & Stanislav Simeonov & Ivan Torlakov, 2020. "On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    12. Briozzo, C.B., 2024. "A generic impulsive controller for Hamiltonian time-independent systems," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    13. Briozzo, Carlos B., 2021. "A generic impulsive controller for hamiltonian linear time-periodic systems," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    14. Mirzaee, Alireza & Dehghani, Maryam & Mohammadi, Mohsen, 2021. "Optimal impulsive blood glucose control through multiple injections," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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