On dynamic feedback linearization

Abstract

We address the problem of transforming a nonlinear multi-input system into a linear controllable one via nonsingular dynamic feedback and (extended) state space diffeomorphism. We show that, in the single input case, if a system is dynamic feedback linearizable it is also static feedback linearizable. We then give sufficient conditions for a class of multi-input systems to be dynamic feedback linearizable. All three-dimensional systems with two controls and a controllable linear approximation about the origin are shown to belong to such a class.