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Tractable stability analysis for systems containing repeated scalar slope-restricted nonlinearities

Tractable stability analysis for systems containing repeated scalar slope-restricted nonlinearities
Tractable stability analysis for systems containing repeated scalar slope-restricted nonlinearities

This paper proposes an LMI-based approach for studying the stability of feedback interconnections of a finite dimensional LTI system and a nonlinear element that consists of several identical scalar nonlinearities that have restrictions on their sector and slope. The results are based on the integral quadratic constraint stability analysis framework and other recent results that give a sharp characterisation of stability multipliers for monotone, repeated scalar nonlinearities. Several examples show the effectiveness of the proposed approach; the lack of conservatism in the results is noteworthy.

absolute stability, anti-windup, integral quadratic constraints, sector bounds, slope-restricted nonlinearity
1049-8923
971-986
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Kerr, Murray L.
76b8a9fa-3b7a-433d-90c8-61a3570f3475
Sofrony, Jorge
20f54d8e-0d5f-4a8a-be1e-61f4052f30ff
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Kerr, Murray L.
76b8a9fa-3b7a-433d-90c8-61a3570f3475
Sofrony, Jorge
20f54d8e-0d5f-4a8a-be1e-61f4052f30ff

Turner, Matthew C., Kerr, Murray L. and Sofrony, Jorge (2015) Tractable stability analysis for systems containing repeated scalar slope-restricted nonlinearities. International Journal of Robust and Nonlinear Control, 25 (7), 971-986. (doi:10.1002/rnc.3122).

Record type: Article

Abstract

This paper proposes an LMI-based approach for studying the stability of feedback interconnections of a finite dimensional LTI system and a nonlinear element that consists of several identical scalar nonlinearities that have restrictions on their sector and slope. The results are based on the integral quadratic constraint stability analysis framework and other recent results that give a sharp characterisation of stability multipliers for monotone, repeated scalar nonlinearities. Several examples show the effectiveness of the proposed approach; the lack of conservatism in the results is noteworthy.

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More information

e-pub ahead of print date: 12 December 2013
Published date: 2015
Keywords: absolute stability, anti-windup, integral quadratic constraints, sector bounds, slope-restricted nonlinearity

Identifiers

Local EPrints ID: 439229
URI: http://eprints.soton.ac.uk/id/eprint/439229
ISSN: 1049-8923
PURE UUID: b27685c8-04ff-4f8d-99d1-c425d15355e9

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Date deposited: 07 Apr 2020 16:30
Last modified: 07 Oct 2020 00:39

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Contributors

Author: Matthew C. Turner
Author: Murray L. Kerr
Author: Jorge Sofrony

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