Local Transverse Feedback Linearization with Partial Information for Single-Input Systems

Given a single-input control-affine system with measured output and controlled invariant submanifold in the system's state space, we present necessary and sufficient conditions for the existence of a local, measurable, transverse output. The measurable transverse output can be used to show feedback equivalence to a system whose dynamics transversal to the submanifold are linear and controllable. This work is motivated by recent results on output feedback and we show how the existence of a measurable transverse output can be applied to solve a robust path following problem.