Razumikhin-type theorem for stochastic functional differential systems via vector Lyapunov function

Liu, Lie and Mao, Xuerong and Cao, Jinde (2019) Razumikhin-type theorem for stochastic functional differential systems via vector Lyapunov function. Journal of Mathematical Analysis and Applications, 479 (2). pp. 1986-2006. ISSN 0022-247X (https://doi.org/10.1016/j.jmaa.2019.07.037)

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Abstract

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.

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