Nearly time optimal stabilizing patchy feedbacks

  • Fabio Ancona

    Dipartimento di Matematica and C.I.R.A.M., Università di Bologna, Piazza Porta S. Donato 5, Bologna 40127, Italy
  • Alberto Bressan

    Department of Mathematics, Penn State University, University Park, PA 16802, USA


We consider the time optimal stabilization problem for a nonlinear control system . Let be the minimum time needed to steer the system from the state to the origin, and call the set of initial states that can be steered to the origin in time . Given any , in this paper we construct a patchy feedback such that every solution of , reaches an -neighborhood of the origin within time .


On considère un problème de stabilization en temps optimal pour un système de commandé non-linéaire du type . Notons par le temps minimal nécessaire pour aller de à l'origine, et par l'ensemble des tels que . Pour chaque , on construit un feedback de type patchy tel que toutes les solutions de , atteignent un -voisinage de l'origine en temps au plus .

Cite this article

Fabio Ancona, Alberto Bressan, Nearly time optimal stabilizing patchy feedbacks. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 2, pp. 279–310

DOI 10.1016/J.ANIHPC.2006.03.010