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Further results on exponential stability for impulsive switched nonlinear time-delay systems with delayed impulse effects

Author

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  • Gao, Lijun
  • Wang, Dandan
  • Wang, Gang

Abstract

This paper is concerned with the problem of exponential stability for a class of impulsive switched nonlinear time-delay systems with delayed impulse effects. By using the multiple Lyapunov–Krasovskii functionals technique, some exponential stability criteria are obtained, respectively, for two kinds of impulsive signals (destabilizing impulsive signal and stabilizing impulsive signal). The derived results not only characterise the effects of delayed impulse, time delay and switching on nonlinear systems, but also remove some restriction conditions. Furthermore, a more precise bound of system state is given. Compared with existing results on related problems, the obtained results are less conservative. Three examples are provided to illustrate the effectiveness and the generality of the proposed results.

Suggested Citation

  • Gao, Lijun & Wang, Dandan & Wang, Gang, 2015. "Further results on exponential stability for impulsive switched nonlinear time-delay systems with delayed impulse effects," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 186-200.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:186-200
    DOI: 10.1016/j.amc.2015.06.023
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    Cited by:

    1. Aziz Khan & Yongjin Li & Kamal Shah & Tahir Saeed Khan, 2017. "On Coupled -Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions," Complexity, Hindawi, vol. 2017, pages 1-9, August.
    2. Zakir Ullah & Amjad Ali & Rahmat Ali Khan & Muhammad Iqbal, 2018. "Existence Results To A Class Of Hybrid Fractional Differential Equations," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 2(1), pages 13-17, January.
    3. Gao, Lijun & Wang, Zhenyue & Sun, Tao & Cao, Zhengbao, 2023. "Stability analysis for hybrid deterministic system under delay-dependent impulses uniting properties of edges," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    4. Xiaohui Xu & Huanbin Xue & Yiqiang Peng & Quan Xu & Jibin Yang, 2018. "Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    5. Zhou, Boling & Yang, Yongqing & Xu, Xianyun, 2019. "The group-delay consensus for second-order multi-agent systems by piecewise adaptive pinning control in part of time interval," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 694-708.
    6. Zhang, Jie & Sun, Yuangong, 2021. "Practical exponential stability of discrete-time switched linear positive systems with impulse and all modes unstable," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    7. Yongyi Gu & Fanning Meng, 2019. "Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods," Complexity, Hindawi, vol. 2019, pages 1-11, August.
    8. Wang, Yijing & Zou, Yanchao & Zuo, Zhiqiang & Li, Hongchao, 2016. "Finite-time stabilization of switched nonlinear systems with partial unstable modes," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 172-181.
    9. Teng Ren & Helu Xiao & Zhongbao Zhou & Xinguang Zhang & Lining Xing & Zhongwei Wang & Yujun Cui, 2019. "The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process," Complexity, Hindawi, vol. 2019, pages 1-15, September.
    10. Ju, Yanhao & Sun, Yuangong & Meng, Fanwei, 2020. "Stabilization of switched positive system with impulse and marginally stable subsystems: A mode-dependent dwell time method," Applied Mathematics and Computation, Elsevier, vol. 383(C).

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