On Orbital Stabilization as an alternative to Reference Tracking Control

With the purpose of highlighting the concept of orbital stabilization as an alternative to the reference tracking control methodology, this paper considers simple, informative examples in relation to motion control of an one-degree-of-freedom, double integrator system. In this regard, the notions of (excessive) transverse coordinates, projections operators and the transverse linearization are introduced, and it is illustrated how these can be used both for the design and analysis of orbitally stabilizing feedback controllers.