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Second order conditions for the controllability of nonlinear systems with drift
In this paper we study controllability of control systems in
$\mathbb R^n$ of the form $\dot x=f(x)+\sum_{i=1}^m$ $u_ig_i(x)$ with
$u\in\mathcal U$ compact convex subset of $\mathbb R^n$ with a
rather general target. The symmetric (driftless) case, i.e. $f=0$,
is a very classical topic, and in this case the results on
controllability and Hölder continuity of the minimal time
function $T$ are related to certain properties of the Lie algebra
generated by the $g_i$'s.
Here, we want to extend some results on controllability and Hölder continuity of $T$ to some cases where $f\ne 0$.