A geometrical formulation of the μ-lower bound problem

Kim, J., Bates, D.G. and Postlethwaite, I. (2009) A geometrical formulation of the μ-lower bound problem. IET Control Theory and Applications, 3(4), pp. 465-472. (doi: 10.1049/iet-cta.2007.0391)

Abstract

A new problem formulation for the structured singular value μ in the case of purely real (possibly repeated) uncertainties is presented. The approach is based on a geometrical interpretation of the singularity constraint arising in the μ lower bound problem. An interesting feature of this problem formulation is that the resulting parametric search space is independent of the number of times any parameter is repeated in the structured uncertainty matrix. A corresponding lower bound algorithm combining randomisation and optimisation methods is developed, and some probabilistic performance guarantees are derived. The potential usefulness of the proposed approach is demonstrated on two high-order real μ analysis problems from the aerospace and systems biology literature.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kim, Dr Jongrae
• Authors: Kim, J., Bates, D.G., and Postlethwaite, I.
• Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
• College/School: College of Science and Engineering > School of Engineering > Biomedical Engineering
• Journal Name: IET Control Theory and Applications
• Publisher: Institution of Engineering and Technology
• ISSN: 1751-8644
• Copyright Holders: Copyright © 2009 Institution of Engineering and Technology
• First Published: First published in IET Control Theory and Applications 3(4):465-472
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.