  This paper addresses the safe stabilization problem of stochastic nonlinear
time-delay systems. Based on theKrasovskii approach, we first propose a
stochastic control Lyapunov-Krasovskii functional to guarantee the
stabilization objective and a stochastic control barrier-Krasovskii functional
to ensure the safety objective. Both functionals are developed respectively for
each control objectives for the first time. Since the optimization problem is
not easy to be resolved for stochastic time-delay systems, we derive a sliding
mode based approach to combine the proposed two functionals and to mediate
stabilization and safety objectives, which allows to achieve the stabilization
objective under the safety requirement. The proposed approach is illustrated
via a numerical example.
