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Invariant measures and controllability of finite systems oncompact manifolds

Published online by Cambridge University Press:  14 September 2011

Philippe Jouan
Philippe Jouan*
Affiliation:
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
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Abstract

A control system is said to be finite if the Lie algebra generated by its vector fieldsis finite dimensional. Sufficient conditions for such a system on a compact manifold to becontrollable are stated in terms of its Lie algebra. The proofs make use of theequivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010)956–973]. and of the existence of an invariant measure on certain compact homogeneousspaces.

Keywords

Compact homogeneous spaceslinear systemscontrollabilityfinite dimensional Lie algebrasHaar measure
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 3 , July 2012 , pp. 643 - 655
Copyright
© EDP Sciences, SMAI, 2011

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