Stability Margin Optimization via Interpolation and Conformal Mappings

©1995 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: 10.1109/9.388685Many interesting problems of robust stabilization can be solved using the complex function theoretic approach of Khargonekar and Tannenbaum (1985). This method is based on the construction of a conformal mapping which reduces the original robust stabilization problem to a Nevanlinna-Pick interpolation problem. The main difficulty of this approach lies in the construction the conformal mapping. The authors present a new numerical algorithm to construct such conformal mappings. Then they demonstrate its effectiveness in the synthesis of optimal gain-phase margin controllers