Abstract: The paper studies the state feedback stabilization of a class of non-autonomous stochastic time-delay sys- tems. On the one hand, due to the intrinsic characteristics of system model (e.g., complex nonlinearity, randomness and non-autonomous), a time-varying feedback controller together with a state feedback control scheme is designed via the backstepping method. On the other hand, based on Razumikhin-type stochastic stability theorem, we analyze the global asymptotic stability in the sense of probability for the closed-loop system with weaker conditions on time-delay.  Final- ly, two simulation examples are presented to illustrate the effectiveness of the proposed feedback controller and control scheme.

Key words: Non-autonomous stochastic system , Time-delay  Backstepping  Razumikhin approach , State feedback