A local stabilizing control scheme using an approximate feedback linearization

We present a method of stabilizing single-input (approximately) feedback linearizable systems in the generic situation where the linearizing feedback and coordinate transformation map are not directly available. In obtaining a stabilizing feedback, we utilize a technique of an approximate feedback linearization which is based on an approximate integrating factor calculated from a recursive algorithm. We construct a feedback controller for the approximately linearized system so that the system is asymptotically stable in a neighborhood of the origin where the one-to-one relation holds with the original coordinate system