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

摘要

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. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.