H∞-controller degree bounds by interpolation theory

In this paper we derive an upper bound for the McMillan degree of all H^∞-optimal controllers using vector interpolation theory. Our analysis will be confined to problems which may be embedded in Fig.1. We will also assume that both P12(s) and P21(s) are square. We will demonstrate that the interpolation theory approach is more direct, and circumvents a number of technical difficulties which have to be overcome using an alternative approach[13]. As a by product, we obtain a new result on the degree of all optimal solutions to the matrix Nevanlinna-Pick problem. A more detailed account of this work will appear shortly in a journal paper[14].