Discrete‐time systems with slope restricted nonlinearities: Zames–Falb multiplier analysis using external positivity
Discrete‐time systems with slope restricted nonlinearities: Zames–Falb multiplier analysis using external positivity
This article exploits positive systems theory in the search for Zames–Falb multipliers for the analysis of discrete‐time Lurie systems, where the nonlinearity is assumed to be slope‐restricted. Although a similar problem has been tackled in a continuous time context, the results in discrete‐time take a different form and require a somewhat different approach to overcome certain technical problems. The work has two compelling features: (i) the arising algorithms are completely convex; and (ii) numerical results compare well with the state‐of‐the‐art in some cases, providing the least conservative result in one instance.
absolute stability, integral quadratic constraints, robust control
2255-2273
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Drummond, Ross
54d0e246-7c22-49da-a6d6-1b8b81b5790c
April 2021
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Drummond, Ross
54d0e246-7c22-49da-a6d6-1b8b81b5790c
Turner, Matthew C. and Drummond, Ross
(2021)
Discrete‐time systems with slope restricted nonlinearities: Zames–Falb multiplier analysis using external positivity.
International Journal of Robust and Nonlinear Control, 31 (6), .
(doi:10.1002/rnc.5391).
Abstract
This article exploits positive systems theory in the search for Zames–Falb multipliers for the analysis of discrete‐time Lurie systems, where the nonlinearity is assumed to be slope‐restricted. Although a similar problem has been tackled in a continuous time context, the results in discrete‐time take a different form and require a somewhat different approach to overcome certain technical problems. The work has two compelling features: (i) the arising algorithms are completely convex; and (ii) numerical results compare well with the state‐of‐the‐art in some cases, providing the least conservative result in one instance.
Text
DTpositive_paper_ZFPY_corrected_bw
- Accepted Manuscript
More information
Accepted/In Press date: 9 December 2020
e-pub ahead of print date: 24 January 2021
Published date: April 2021
Additional Information:
Funding Information:
The authors thank the anonymous reviewers for their comments and suggestions, which greatly improved the contents of this article. This work was supported by the Major State Basic Research Development Program of China (2012CB720500), the National Natural Science Foundation of China (61333010, 61222303, and 61422303) and the Natural Science Foundation of Shanghai (16ZR1407300).
Publisher Copyright:
© 2021 John Wiley & Sons, Ltd.
Keywords:
absolute stability, integral quadratic constraints, robust control
Identifiers
Local EPrints ID: 446645
URI: http://eprints.soton.ac.uk/id/eprint/446645
ISSN: 1049-8923
PURE UUID: 47006dd0-2a64-46e6-91b7-43a34f123bd9
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Date deposited: 17 Feb 2021 17:30
Last modified: 17 Mar 2024 06:21
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Author:
Matthew C. Turner
Author:
Ross Drummond
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