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The paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced by the authors to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robustness of patchy feedback controls in the presence of measurement errors and external disturbances.doi:10.1137/s0363012901391676 fatcat:olb3frjyarhsxc63ikuxfjvs34