Weight Selection in Interpolation with a Dimensionality Constraint

The topic of the paper relates to a recent parametrization of analytic interpolants with a bound on their dimension, as solutions to certain weighted entropy minimization problems. The analytic interpolation problem arises in the context of shaping closed-loop transfer functions via a suitable choice of controller. Our goal is to shed light on how the choice of weights affects the shape of the corresponding closed-loop transfer functions. Further, given a desirable shape, we indicate how a suitable weight can be obtained as a solution of a certain quasi-convex problem