Asymptotic tracking of periodic trajectories for a particle in an elliptical billiards

An infinitely rigid unitary mass (particle) is considered, moving on a planar region delimited by a rigid elliptical barrier (elliptical billiards) under the action of proper control forces. A class of periodic trajectories, involving an infinite sequence of nonsmooth impacts between the mass and the barrier at fixed times, is found by using an LMIs based procedure and a tracking problem is stated and solved by means of a controller whose state is subject to jumps.