Journal of Convex Analysis 09 (2002), No. 2, 535--542
Copyright 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
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