The current literature on the global state feedback stabilization of nonlinear systems
modeled by a perturbed chain of nonlinear integrators, particularly those whose linearization about
the origin may contain uncontrollable modes, essentially contains two methods: a smooth controller
scheme (only under strict assumptions) and a non-smooth one. The most general of these systems
could previously only be globally asymptotically stabilized by continuous time-invariant state feedback
controller, where this paper shows that now at least C1 stabilization can be achieved, upon
existence, in this more general setting. This new method can be seen as not only a natural unification
of the smooth and nonsmooth methods, but also a generalization to construct smoother stabilizers.