Tracking in the presence of a time-varying uncertain gain

In this paper we consider the use of linear periodic controllers to solve a tracking problem in the face of time-varying multiplicative gain uncertainty. The class of signals to be tracked is modelled by a (stable) filter on the reference input.We show, under the technical assumption that the relative degree of the filter is greater than the plant, that there exists a linear periodic controller which can provide near-optimal linear time-invariant performance for every admissible gain.