FEEDBACK LINEARIZATION AND DRIFTLESS SYSTEMS

The problem of dynamic feedback linearization is recast using the noti on of dynamic immersion. We investigate here a ''generic'' property wh ich holds at every point of a dense open subset, but may fail at some points of interest, such as equilibrium points. Linearizable systems a re then systems that can be immersed into linear controllable ones. Th is 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 equ als two. Though noninvertible feedbacks are not a priori excluded, it turns out that linearizable driftless systems with two inputs can be l inearized 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 syst ems.