Abstract: A differential equation with discontinuous right-hand side would appear in general to be unduly sensitive to initial conditions, or to the presence of perturbation or error terms. For this reason, one might doubt that discontinuous stabilizing feedback would be effective in the presence of such terms. Yet a large class of such feedbacks (constructed geometrically through proximal analysis) has desirable features in this regard. We describe this, as well as another design approach via subgradients which leads to a stabilizing feedback which is nearly continuous.