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

Abstract

This paper mainly focuses on the pth ($p\ge 2$)-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 pth ($p\ge 2$)-moment ISS reduces to the pth ($p\ge 2$)-moment practical exponential stability and the pth ($p\ge 2$)-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.

Keywords:

• Neutral stochastic differential equations
• stability
• time-varying delay
• input-to-state
• Lévy noise

2010 AMS SUBJECT CLASSIFICATIONS:

• 60H10
• 60H15
• 34K20
• 34K50

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (62163027) and the Natural Science Foundation of Jiangxi Province of China (20171BCB23001).