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Feedback linearization and driftless systems

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Abstract

The problem of dynamic feedback linearization is recast using the notion of dynamic immersion. We investigate here a “generic” property which holds at every point of a dense open subset, but may fail at some points of interest, such as equilibrium points. Linearizable systems are then systems that can be immersed into linear controllable ones. This setting is used to study the linearization of driftless systems: a geometric sufficient condition in terms of Lie brackets is given; this condition is also shown to be necessary when the number of inputs equals two. Though noninvertible feedbacks are nota priori excluded, it turns out that linearizable driftless systems with two inputs can be linearized using only invertible feedbacks, and can also be put into a chained form by (invertible) static feedback. Most of the developments are done within the framework of differential forms and Pfaffian systems.

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Authors and Affiliations

  1. Centre Automatique et Systèmes, École des Mines de Paris, 35 rue Saint-Honoré, 77305, Fontainebleau Cedex, France

    Philippe Martin

  2. Centre Automatique et Systèmes, École des Mines de Paris, 60 Bd Saint-Michel, 75272, Paris Cedex 06, France

    Pierre Rouchon

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  1. Philippe Martin
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Additional information

This work was partially supported by INRIA, NSF Grant ECS-9203491, GR “Automatique” (CNRS), and DRED (Ministère de l'Éducation Nationale). Part of it was done while the first author was visiting the Center for Control Engineering and Computation, University of California at Santa Barbara.

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Martin, P., Rouchon, P. Feedback linearization and driftless systems. Math. Control Signal Systems 7, 235–254 (1994). https://doi.org/10.1007/BF01212271

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