Robust asymptotic tracking of periodic trajectories in elliptical billiards

An infinitely rigid mass subject to friction, with mass and linear damping factor being in general not known exactly, is considered, moving on a planar region delimited by a rigid elliptical barrier (
elliptical

billiards
) under the action of proper control forces. The robust tracking control problem for a class of periodic trajectories, involving nonsmooth impacts between the mass and the barrier at fixed times is stated and solved by means of a controller based on the internal model principle and whose state is subject to discontinuities.