An interpolation theory approach to H_∞ controller degree bounds

We derive upper bounds for the McMillan degree of all P-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 Nevanfinna-Pick problem.