Inserted: 14 oct 2021
Last Updated: 27 oct 2021
We say that a control system is locally controllable if the attainable set from any state x contains an open neighborhood of x, while it is controllable if the attainable set from any state is the entire state manifold. Quite surprisingly, the question of whether local controllability implies global controllability seems not to have been considered in the literature. We show in this paper that a control system satisfying local controllability is controllable.