An exterior differential characterization of single-input local transverse feedback linearization

Abstract

Given a nonlinear control affine system and a point on a controlled invariant, embedded submanifold of the system’s state-space, the local transverse feedback linearization problem is to feedback linearize the portion of the system’s dynamics governing its transversal motion with respect to the given submanifold. This work characterizes necessary and sufficient conditions for a single-input system to be locally transversally feedback linearizable to such a submanifold in terms of exterior differential systems.