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

Abstract The main aim of this paper is to investigate the asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Levy 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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