The paper addresses the problem of the global stabilization by means of continuous feedback of a class of nonlinear (possibly non-affine and nonsmooth) systems which in general cannot be stabilized by smooth (i.e., at least ) feedback. The basic result concerns systems which can be represented as a chain of power integrators perturbed by a vector field in triangular form
where the ’s are odd, the are unknown but constrained to a bounded interval, and
( stands for ). The functions are subject to some other technical assumptions. The proof is based on an iterative procedure and exploits the theory of homogeneous systems. It uses the method of adding a power integrator in order to explicitly construct a continuous feedback and generate a Lyapunov function. The paper contains also some extensions of the basic result and a rich variety of interesting examples.