| Issue |
ESAIM: COCV
Volume 18, Number 3, July-September 2012
|
|
|---|---|---|
| Page(s) | 643 - 655 | |
| DOI | https://doi.org/10.1051/cocv/2011165 | |
| Published online | 14 September 2011 | |
Invariant measures and controllability of finite systems on compact manifolds
Lab. R. Salem, CNRS UMR 6085, Université de Rouen, avenue de
l’Université, BP
12, 76801
Saint-Étienne-du-Rouvray,
France
Philippe.Jouan@univ-rouen.fr
Received:
11
February
2011
Revised:
19
April
2011
A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
Mathematics Subject Classification: 17B66 / 37A05 / 37N35 / 93B05 / 93B17 / 93C10
Key words: Compact homogeneous spaces / linear systems / controllability / finite dimensional Lie algebras / Haar measure
© EDP Sciences, SMAI, 2011
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