Stabilization of nonlinear systems with delay in the input through backstepping

We propose a new solution to the problem of globally asymptotically stabilizing a nonlinear system in feedback form with a known pointwise delay in the input. The result covers a family of systems wider than those studied in the literature and endows with control laws with a single delay, in contrast to the existing one, which include two distinct pointwise delays or distributed delays. The design strategy is based on the construction of an appropriate Lyapunov-Krasovskii functional.