An expanded method to robustly stabilize uncertain nonlinear systems

Abstract

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.