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.

ORCID iDs

Liu, Lie, Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864 and Cao, Jinde;
CORE (COnnecting REpositories)