Invariant measures and controllability of finite systems on compact manifolds
Lab. R. Salem, CNRS UMR 6085, Université de Rouen, avenue de
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