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Stability analysis for hybrid deterministic system under delay-dependent impulses uniting properties of edges

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  • Gao, Lijun
  • Wang, Zhenyue
  • Sun, Tao
  • Cao, Zhengbao

Abstract

In this summary, for a kind of hybrid deterministic system, we emphasize the input-to-state stability (ISS) property. Meanwhile, the delay-dependent impulse and switching behavior are permitted to arise asynchronously. In other words, the impulses can arise many times or not once within a period of switching interval. For impulsive signals, A fresh idea called admissible edge-dependent average impulsive interval (AED-AII) is addressed according to properties of edges. By developing the multiple Lyapunov-Krasovskii functionals (MLKFs), merged with the AED-ADT switching scheme and AED-AII method, some ameliorated criteria in accordance with the ISS of hybrid delayed systems are established with regard to stabilizing and destabilizing impulses. Compared with previous work, our setup enjoys the important features: the candidate functions fully taps the effect of the delay existing in the system dynamics and impulse on the function part of the MLKFs; the AED-AII method combined with the AED-ADT switching scheme in our paper contains a larger group of the impulsive and switching signals; and for the case in which all the subsystems are unstable, the stability criterion is suitable for the arbitrary time delay. Finally, an example shows that the results of this paper are effective.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:444:y:2023:i:c:s0096300322008724
    DOI: 10.1016/j.amc.2022.127804
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    References listed on IDEAS

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    1. Zhai, Ding & Lu, An-Yang & Li, Jing-Hao & Zhang, Qing-Ling, 2016. "Simultaneous fault detection and control for switched linear systems with mode-dependent average dwell-time," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 767-792.
    2. Jian Li & Guang-Hong Yang, 2016. "Simultaneous fault detection and control for switched systems with actuator faults," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2411-2427, July.
    3. Cao, Zhengbao & Gao, Lijun & Wang, Gang, 2019. "Stability conditions of switched nonlinear systems with unstable subsystems and destabilizing switching behaviors," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    4. 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.
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