Feedback Linearization of Transverse Dynamics for Periodic Orbits

Andrzej Banaszuk, Georgia Tech

We give necessary and sufficient conditions for feedback linearization of the transverse dynamics (TFL) of a nonlinear affine single-input system in a neighborhood of a periodic orbit. The TFL procedure provides a means of finding coordinates that are tuned to the structure of the control system with respect to the periodic orbit. An autonomous feedback control providing exponential stability of the periodic orbit is easily designed in the transverse coordinate system. We also show how one can linearize the transverse dynamics of a nonlinear affine single-input system in R3 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.