This paper deals with the stability problem for non-holonomic systems and describes a sufficient condition for the existence of a time-varying switching control scheme which globally asymptotically stabilizes the zero equilibrium. The sufficient condition is based on a new concept of Lyapunov function for hybrid systems which is used in the demonstration of a stability theorem. The new idea is also put in relation with known theoretical tools such as a multiple Lyapunov function and a common Lyapunov function. Finally, a simple example of a non-holonomic system is taken into account, for which the existence of a stabilizing switching control law is proven. The results of some simulations are also reported in order to evaluate qualitatively the effecrtiveness of the method.
