A universal method for robust stabilization of nonlinear systems: unification and extension of smooth and non-smooth approaches

The current literature on the stabilization of nonlinear systems, particularly those whose linearization about the origin may contain uncontrollable modes, essentially contains two distinct methods: a smooth controller scheme (only under strict assumptions) and a non-smooth one. This paper introduces a more general setting under which: 1) unification of the two aforementioned schemes is achieved and 2) it is possible to find a continuously differentiable control law for some systems previously only stabilizable by a continuous controller. This new method is implicitly based on the ideas of homogeneous systems theory and the adding a power integrator technique