  This paper studies the stabilization and safety problems of nonlinear
time-delay systems, where time delays exist in system state and affect the
controller design. Following the Razumikhin approach, we propose a novel
control Lyapunov-Razumikhin function to facilitate the controller design and to
achieve the stabilization objective. To ensure the safety objective, we propose
a Razumikhin-type control barrier function for time-delay systems for the first
time. Furthermore, the proposed Razumikhin-type control Lyapunov and barrier
functions are merged such that the stabilization and safety control design can
be combined to address the stabilization and safety simultaneously, which
further extends the control design from the delay-free case into the time-delay
case. Finally, the proposed approach is illustrated via a numerical example.
