# Local controllability does imply global controllability

arXiv: https://arxiv.org/abs/2110.06631 · HTML: https://mlsanity.com/paper/2110.06631/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2021.

## Built on by (most cited first, 2 of 2)

- [Online Stackelberg Optimization via Nonlinear Control](https://mlsanity.com/paper/2406.18805/) (2024)
- [Controller Design for Structured State-space Models via Contraction Theory](https://mlsanity.com/paper/2604.07069/) (2026)

## Abstract (arXiv)

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. We show in this note that a control system satisfying local controllability is controllable. Our self-contained proof is alternative to the combination of two previous results by Kevin Grasse.