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
1079-1100
Sefton, J. A.
f4e2c83b-2df6-47d5-94a8-5a44fdc32f2f
Ober, R. J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
July 1993
Sefton, J. A.
f4e2c83b-2df6-47d5-94a8-5a44fdc32f2f
Ober, R. J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
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
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Local EPrints ID: 425004
URI: http://eprints.soton.ac.uk/id/eprint/425004
ISSN: 0005-1098
PURE UUID: ba642816-3df7-4cc2-9924-ddce48df4136
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Date deposited: 09 Oct 2018 16:30
Last modified: 16 Mar 2024 04:37
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Author:
J. A. Sefton
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