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

with the controllability of a perturbed version

\dot x(t) \in F_n(x(t)) x ˙ ( t ) ∈ F n ( x ( t ) )

. The reference (or nominal) convex process

F F

is seen as the “limit” of a sequence

\{F_n\}_{n\in \mathbb{N}} { F n } n ∈ N

of approximations.