Dual Conditions for Local Transverse Feedback Linearization

D’Souza, R. S., & Nielsen, C. (2018). Dual Conditions for Local Transverse Feedback Linearization. 2018 IEEE Conference on Decision and Control (CDC), 2938–2943. https://doi.org/10.1109/CDC.2018.8619815Given a control-affine system and a controlled invariant submanifold, the local transverse feedback linearization problem is to determine whether or not the system is locally feedback equivalent to a system whose dynamics transversal to the submanifold are linear and controllable. In this paper we present necessary and sufficient conditions for a single-input system to be locally transversally feedback linearizable to a given submanifold that dualize, in an algebraic sense, previously published conditions. These dual conditions are of interest in their own right and represent a first step towards a Gardner-Shadwick like algorithm for local transverse feedback linearization