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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.

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

Identifiers

Local EPrints ID: 425004
URI: https://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

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Date deposited: 09 Oct 2018 16:30
Last modified: 14 Mar 2019 01:21

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Contributors

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

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