Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Next Article Journal of Convex Analysis 09 (2002), No. 2, 535--542Copyright Heldermann Verlag 2002 Rank Condition and Controllability of Parametric Convex Processes Phillipe Lavilledieu Dép. des Mathématiques, Université d'Avignon, 33 Rue Louis Pasteur, 84000 Avignon, France phillipe.lavilledieu@univ-avignon.fr Alberto Seeger Dép. des Mathématiques, Université d'Avignon, 33 Rue Louis Pasteur, 84000 Avignon, France alberto.seeger@univ-avignon.fr [Abstract-pdf] This note is concerned with the controllability of differential inclusions whose right-hand sides are convex processes. More precisely, it relates the controllability of $\dot x(t) \in F(x(t))$ with the controllability of a perturbed version $\dot x(t) \in F_n(x(t))$. The reference (or nominal) convex process $F$ is seen as the limit'' of a sequence $\{F_n\}_{n\in \mathbb{N}}$ of approximations. Keywords: Convex process, differential inclusion, controllability, point spectrum, rank condition, Painlevé-Kuratowski convergence. MSC: 93B05; 47H04, 34A60 [ Fulltext-pdf  (227  KB)]