Stability of control systems and graphs of linear systems
Stability of control systems and graphs of linear systems
New conditions for internal stability of a closed-loop control system are given in terms of the graphs of the multiplication operators induced by the transfer functions of the plant and the controller. These conditions can be given a geometrical interpretation. This relates closed-loop stability to the minimal angle between the graph space associated with the system and the graph space associated with the controller. The maximally stabilizing controller is defined as the controller that maximizes the minimum angle between the graph space associated with the system and the graph space associated with the controller. It is shown that this controller can be calculated as a Nehari extension of the coprime factors of the system.
gap metric, graphs of operators, Internal stability, robust control
265-280
Ober, R. J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Sefton, J. A.
f4e2c83b-2df6-47d5-94a8-5a44fdc32f2f
October 1991
Ober, R. J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Sefton, J. A.
f4e2c83b-2df6-47d5-94a8-5a44fdc32f2f
Ober, R. J. and Sefton, J. A.
(1991)
Stability of control systems and graphs of linear systems.
Systems and Control Letters, 17 (4), .
(doi:10.1016/0167-6911(91)90142-2).
Abstract
New conditions for internal stability of a closed-loop control system are given in terms of the graphs of the multiplication operators induced by the transfer functions of the plant and the controller. These conditions can be given a geometrical interpretation. This relates closed-loop stability to the minimal angle between the graph space associated with the system and the graph space associated with the controller. The maximally stabilizing controller is defined as the controller that maximizes the minimum angle between the graph space associated with the system and the graph space associated with the controller. It is shown that this controller can be calculated as a Nehari extension of the coprime factors of the system.
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Published date: October 1991
Keywords:
gap metric, graphs of operators, Internal stability, robust control
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Local EPrints ID: 425000
URI: http://eprints.soton.ac.uk/id/eprint/425000
ISSN: 0167-6911
PURE UUID: 91122fd8-6cd6-44a6-8dc6-ec5c061e4371
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Date deposited: 09 Oct 2018 16:30
Last modified: 06 Jun 2024 02:04
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Author:
J. A. Sefton
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