The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise

Wei Mao, Liangjian Hu, Xuerong Mao

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Abstract

The main aim of this paper is to investigate the asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise (HSSwPDLNs). Under the local Lipschitz condition and non-linear growth condition, we investigate the existence and uniqueness of the solution to HSSwPDLNs. By using the Lyapunov functions and M-matrix theory, we establish some sufficient conditions on the asymptotic stability and polynomial stability for HSSwPDLNs. Finally, two examples are provided to illustrate our results.
Original languageEnglish
Pages (from-to)1174-1198
Number of pages25
JournalJournal of the Franklin Institute
Volume357
Issue number2
Early online date5 Dec 2019
DOIs
Publication statusPublished - 31 Jan 2020

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Keywords

  • hybrid stochastic systems
  • pantograph delay
  • non-Gaussian Lévy noise
  • asymptotic stability
  • polynomial stability

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