The University of Southampton
University of Southampton Institutional Repository

Uncertainty in the weighted gap metric: A geometric approach

Uncertainty in the weighted gap metric: A geometric approach
Uncertainty in the weighted gap metric: A geometric approach

The stability of control systems is studied in the context of weighted input-output signal spaces. Necessary and sufficient conditions for a controller to stabilize a plant are given in terms of geometric notions. These geometric quantities can be calculated by solving H optimization problems. Maximally stabilizing controllers in a weighted signal space are introduced and characterized in terms of Nehari extensions. The robustness properties of maximally stabilizing controllers are analysed in terms of weighted coprime factor uncertainty. Necessary and sufficient conditions are established for a controller of a given plant to be the maximally stabilizing controller of the plant with respect to a weight. An upper bound for the mixed-sensitivity of a control system is given where the controller is the maximally stabilizing controller of the plant.

Control theory, frequency domain, multivariable systems, robust control
0005-1098
1079-1100
Sefton, J. A.
f4e2c83b-2df6-47d5-94a8-5a44fdc32f2f
Ober, R. J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Sefton, J. A.
f4e2c83b-2df6-47d5-94a8-5a44fdc32f2f
Ober, R. J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36

Sefton, J. A. and Ober, R. J. (1993) Uncertainty in the weighted gap metric: A geometric approach. Automatica, 29 (4), 1079-1100. (doi:10.1016/0005-1098(93)90108-6).

Record type: Article

Abstract

The stability of control systems is studied in the context of weighted input-output signal spaces. Necessary and sufficient conditions for a controller to stabilize a plant are given in terms of geometric notions. These geometric quantities can be calculated by solving H optimization problems. Maximally stabilizing controllers in a weighted signal space are introduced and characterized in terms of Nehari extensions. The robustness properties of maximally stabilizing controllers are analysed in terms of weighted coprime factor uncertainty. Necessary and sufficient conditions are established for a controller of a given plant to be the maximally stabilizing controller of the plant with respect to a weight. An upper bound for the mixed-sensitivity of a control system is given where the controller is the maximally stabilizing controller of the plant.

This record has no associated files available for download.

More information

Published date: July 1993
Keywords: Control theory, frequency domain, multivariable systems, robust control

Identifiers

Local EPrints ID: 425004
URI: http://eprints.soton.ac.uk/id/eprint/425004
ISSN: 0005-1098
PURE UUID: ba642816-3df7-4cc2-9924-ddce48df4136
ORCID for R. J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

Catalogue record

Date deposited: 09 Oct 2018 16:30
Last modified: 16 Mar 2024 04:37

Export record

Altmetrics

Contributors

Author: J. A. Sefton
Author: R. J. Ober ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×