On the stabilization of nonholonomic systems

We discuss the issue of local (global) stabilizability of nonholonomic systems. We show that if a nonholonomic system with less inputs as states presents certain geometric features, mainly the existence of a controlled invariant distribution, and if it is non continuous, it is possible to design a locally (globally) stabilizing continuously differentiable (smooth) control law around a point of discontinuity. The main contribution of the paper rests on a sufficient condition for stabilizability of discontinuous nonholonomic systems and on the use of a non-smooth coordinate transformation to overcome the obstruction of stabilizability contained in Brockett´s theorem