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Stability of control systems and graphs of linear systems

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
0167-6911
265-280
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.
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), 265-280. (doi:10.1016/0167-6911(91)90142-2).

Record type: Article

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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More information

Published date: October 1991
Keywords: gap metric, graphs of operators, Internal stability, robust control

Identifiers

Local EPrints ID: 425000
URI: http://eprints.soton.ac.uk/id/eprint/425000
ISSN: 0167-6911
PURE UUID: 91122fd8-6cd6-44a6-8dc6-ec5c061e4371
ORCID for R. J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

Catalogue record

Date deposited: 09 Oct 2018 16:30
Last modified: 06 Jun 2024 02:04

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Contributors

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

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