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Conic sector analysis using integral quadratic constraints

Conic sector analysis using integral quadratic constraints
Conic sector analysis using integral quadratic constraints

This paper interprets the Conic Sector stability results of Zames, and the multivariable generalizations provided by Safonov and Athans, in an integral quadratic constraint context. The ideas are formulated for the case where one element of a feedback interconnection is linear and the other satisfies a conic sector condition. This scenario allows the main stability results to be formulated using integral quadratic constraints, with all finite-sector cases being captured using this framework. The stability results are expressed using frequency domain inequalities or linear-matrix inequalities. Some examples show how the main technical result can, in the multivariable case, be used to provide a reduction in conservatism over standard results.

absolute stability, conic sector, integral quadratic constraints
1049-8923
741-755
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Forbes, James R.
96c984cf-b086-4588-9654-53ec7a298973
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Forbes, James R.
96c984cf-b086-4588-9654-53ec7a298973

Turner, Matthew C. and Forbes, James R. (2020) Conic sector analysis using integral quadratic constraints. International Journal of Robust and Nonlinear Control, 30 (2), 741-755. (doi:10.1002/rnc.4803).

Record type: Article

Abstract

This paper interprets the Conic Sector stability results of Zames, and the multivariable generalizations provided by Safonov and Athans, in an integral quadratic constraint context. The ideas are formulated for the case where one element of a feedback interconnection is linear and the other satisfies a conic sector condition. This scenario allows the main stability results to be formulated using integral quadratic constraints, with all finite-sector cases being captured using this framework. The stability results are expressed using frequency domain inequalities or linear-matrix inequalities. Some examples show how the main technical result can, in the multivariable case, be used to provide a reduction in conservatism over standard results.

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More information

Accepted/In Press date: 7 October 2019
e-pub ahead of print date: 5 November 2019
Published date: 25 January 2020
Keywords: absolute stability, conic sector, integral quadratic constraints

Identifiers

Local EPrints ID: 439209
URI: http://eprints.soton.ac.uk/id/eprint/439209
ISSN: 1049-8923
PURE UUID: edc30964-a471-4275-a404-1db565559620

Catalogue record

Date deposited: 07 Apr 2020 16:30
Last modified: 25 Nov 2021 18:54

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Contributors

Author: Matthew C. Turner
Author: James R. Forbes

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