Feedback Linearization of Transverse Dynamics for Periodic Orbits in R^3 with Points of Transverse Controllability Loss

In this paper we show how one can linearize the transverse dynamics of a nonlinear affine single-input system in R^3 in a neighborhood of a periodic orbit in the case when the transverse linear controllability fails in finite number of points along the periodic orbit. An autonomous feedback control providing stability of the periodic orbit is designed in the transverse coordinate system.Research supported in part by NSF under grant PYI ECS-9396296, by AFOSR under grant AFOSR 94NM006, and by a grant from Hughes Aircraft Company