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

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.

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