Global linearization by feedback and state transformation

Differential geometric conditions equivalent to the existence of a solution to the global feedback linearization problem are given. If global feedback for linearization is obtained with an atlas of local state space transformations, the resulting closed loop system still has almost all the important features of a linear system. Existence of a compact leaf in any of the standard foliations arising in the local feedback linearization problem is shown to represent nontrivial linear holonomy and hence an obstruction to the existence of global feedback. We prove that in the analytic case, if the state space is simply-connected, this obstruction does not occur. We show that in the two dimensional (C??) case, if the manifold is simply connected, then the local conditions and controllability are sufficient for global feedback linearization.