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This paper mainly focuses on the  p th ()-moment input-to-state stability (ISS) of neutral stochastic delay differential equations (NSDDEs) with Lévy noise and Markovian switching. By using the generalized integral inequality and the Lyapunov function methodology, the ISS, integral input-to-state stability (iISS), and stochastic input-to-state stability (SISS) of such equations are obtained. When the input signal is a constant signal and a zero signal, the  p th ()-moment ISS reduces to the  p th ()-moment practical exponential stability and the  p th ()-moment exponential stability, respectively. Finally, an example of the mass–spring–damping (MSD) model under the stochastic perturbation is given to verify the validity of the results.

Exponential input-to-state stability for neutral stochastic delay differential equations with Lévy noise and Markovian switching