An interpolation theory approach to H^∞ controller degree bounds

We derive upper bounds for the McMillan degree of all H^∞-optimal controllers associated with design problems which may be embedded in a certain generalized regular configuration. Our analysis is confined to problems of the first kind, which are characterized by the assumption that both P₁₂(s) and P₂₁(s) are square but not necessarily of the same size. This paper, which uses interpolation theory, complements a previous paper which addresses the same problem through an approach based on approximation theory. We demonstrate that the interpolation theory approach is more direct and circumvents a number of the technical difficulties in the previous method: the final outcome is a much shorter proof. As a by-product, we achieve a new result on the degree of an optimal solution of the matrix Nevanlinna-Pick problem.