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

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Mao, Wei and Hu, Liangjian and Mao, Xuerong (2020) The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise. Journal of the Franklin Institute, 357 (2). pp. 1174-1198. ISSN 0016-0032 (https://doi.org/10.1016/j.jfranklin.2019.11.068)

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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.

ORCID iDs

Mao, Wei, Hu, Liangjian and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
CORE (COnnecting REpositories)