Rank Condition and Controllability of Parametric Convex Processes

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.