Spectral Nevanlinna-Pick interpolation theory and robust stabilization

©1987 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/CDC.1987.272721In this note we will discuss a new kind of interpolation theory in which one bounds the spectral radius of the matrix-valued interpolating functions instead of the norm as is the case with ordinary Nevanlinna-Pick interpolation. We show how this is related to certain kinds of multivariate stability margin problems of the kind considered by Doyle [2] and Safonov [8]