New results and examples on a class of discontinuous controllers

A discontinuous control law exponentially stabilizing a simple nonholonomic system is discussed and analyzed in detail. Basic properties, such as existence and uniqueness of the closed loop system trajectories, and simple robustness issues are studied. Continuous modifications of the considered discontinuous control law are proposed and discussed in detail. The considered controller is representative of a large class of feedbacks widely used in the literature, for which a precise mathematical analysis is still lacking. One of the goals of this paper is to provide such analysis and to demonstrate that the somewhat informal procedure used in the literature to study this class of controllers yields correct conclusions.