Poincaré Normal Form for a Class of Driftless Systems in a One-Dimensional Submanifold Neighborhood |
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Authors: | D Boutat J-P Barbot |
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Affiliation: | (1) LVR, ENSI-Bourges/Université d'Orléans, 10 Boulevard Lahitolle, 18020 Bourges Cedex, France., FR;(2) Equipe Commande des Systèmes (ECS), ENSEA, 6 avenue du Ponceau, 95014 Cergy Cedex, France. barbot@ensea.fr., FR |
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Abstract: | In this paper, motivated by the restrictive conditions required to obtain an exact chained form, we propose a quadratic normal
form around a one-dimensional equilibrium submanifold for systems which are in a chained form in their first approximation.
In the case considered here, in contrast to the case of approximated feedback linearization, not all the state and input components
have the same approximation meaning. Because of this, we use a very simplified version of dilation, which is a useful way
to design a homogeneous control law for driftless systems.
Date received: December 2, 1999. Date revised: October 24, 2001. |
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Keywords: | , Driftless systems, Poincaré normal forms, Homogeneous diffeomorphisms and feedbacks, Approximated Frobenius theorem,,,,,,Higher-order method, |
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