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Equivalence of control systems with linear systems on Lie groups and homogeneous spaces

Philippe Jouan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only if the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear if its flow is a one parameter group of automorphisms. An affine vector field is obtained by adding a left invariant one. Its projection on a homogeneous space, whenever it exists,...

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