Static and dynamic state feedback linearization

Abstract

The problem of feedback linearization consists in transforming (in a given open domain) a nonlinear system into a linear one by state feedback and state space diffeomorphism. Indeed, such transformations do not exist in general (or rather rarely) but, if they exist, they allow the use of classic linear stabilizing techniques such as pole placement, quadratic synthesis, robust synthesis and so on. The price of such a simplification is paid, on the one hand, by the fact that such transformations are not everywhere defined and may generate a blow-up of controls. On the other hand, the computations of the feedback may be very heavy and digital synthesis may decrease the feedback performances. Finally, the feedback efficiency dramatically depends on the accuracy with which the model represents the real plant.