On the existence and asymptotic stability of hybrid stochastic systems with neutral term and non-differentiable time delay

This paper focuses on a class of hybrid stochastic delay systems with neutral term (HSDSwNT), where the time delay may be non-differentiable and the coefficients may not satisfy the linear growth condition. Under the local Lipschitz condition and the Khasminskii-type condition, the existence and uniqueness as well as boundedness of the solution to the HSDSwNT are established. By virtue of the Lyapunov function method and the M-matrix theory, sufficient conditions on the asymptotic stability and general decay stability are also examined for HSDSwNT. Finally, two examples are given to show the effectiveness of our results