Stabilization by patchy feedbacks and robustness properties

This note is concerned with the problem of robust stabilization of control systems via discontinuous feedback laws. A particular class of discontinuous, piecewise smooth vector fields ("patchy vector fields") was introduced by the authors in a previous paper to construct discontinuous stabilizing feedbacks for globally asymptotically controllable systems. Here we study the stability of the corresponding solution set with respect to impulsive perturbations with small total variation. These results yield the robustness of "patchy feedback controls" in the presence of measurement errors and external disturbances.