Stability rates for patchy vector fields
Dipartimento di Matematica and C.I.R.A.M., Università di Bologna,
Piazza Porta S. Donato 5, Bologna 40127, Italy; firstname.lastname@example.org.
2 S.I.S.S.A., Via Beirut 4, Trieste 34014, Italy; email@example.com.
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 in Ancona and Bressan (1999) 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.
Mathematics Subject Classification: 34A37 / 34D / 93D09 / 93D15
Key words: Patchy vector field / impulsive perturbation.
© EDP Sciences, SMAI, 2004