  This paper studies the stabilization and safety problems of nonlinear
time-delay systems. Following both Razumikhin and Krasovskii approaches, we
propose novel control Lyapunov functions/functionals for the stabilization
problem and novel control barrier functions/functionals for the safety problem.
The proposed control Lyapunov and barrier functions/functionals extend the
existing ones from the delay-free case to the time-delay case, and allow for
designing the stabilizing and safety controllers in closed-form. Since
analytical solutions to time-delay optimal control problems are hard to be
achieved, a sliding mode control based approach is developed to merge the
proposed control Lyapunov and barrier functions/functionals. Based on the
sliding surface functional, a feedback control law is established to
investigate the stabilization and safety objectives simultaneously. In
particular, the properties of the sliding surface functional are analyzed, and
further how to construct the sliding surface functional is discussed. Finally,
the proposed approaches are illustrated via two numerical examples from the
connected cruise control problem of automotive systems and the synchronization
problem of multi-agent systems.
