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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, 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.
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,
(2010)
956–973]. and of the existence of an invariant measure on certain compact homogeneous
spaces.
We consider smooth single-input, two-output systems on a compact manifold X. We show that the set of systems that are observable for any polynomial input whose degree is less than or equal to a given bound contains an open and dense subset of the set of smooth systems.
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,
(2010)
956–973]. and of the existence of an invariant measure on certain compact homogeneous
spaces.
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...
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