This paper is concerned with input-to-state stability of SFDSs. By using stochastic analysis techniques, Razumikhin techniques and vector Lyapunov function method, vector Razumikhin-type theorem has been established on input-to-state stability for SFDSs. Novel sufficient criteria on the pth moment exponential input-to-state stability are obtained by the established vector Razumikhin-type theorem. When input is zero, an improved criterion on exponential stability is obtained. Two examples are provided to demonstrate validity of the obtained results.
- vector Lyapunov function
- razumikhin-type theorems
- input-to-state stability
- exponential stability
- stochastic functional differential equation
Liu, L., Mao, X., & Cao, J. (2019). Razumikhin-type theorem for stochastic functional differential systems via vector Lyapunov function. Journal of Mathematical Analysis and Applications, 479(2), 1986-2006. https://doi.org/10.1016/j.jmaa.2019.07.037