Stability Rates for Patchy Vector Fields

ABSTRACT. This paper is concerned with the stability of the set of trajectories of a "patchy" vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced by the authors to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term.