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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
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.
1049-8923
Turner, Matthew C.
6befa01e-0045-4806-9c91-a107c53acba0
Drummond, Ross
54d0e246-7c22-49da-a6d6-1b8b81b5790c
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. (doi:10.1002/rnc.5391).

Record type: Article

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.

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Accepted/In Press date: 9 December 2020
e-pub ahead of print date: 24 January 2021

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 Feb 2021 17:30

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Contributors

Author: Matthew C. Turner
Author: Ross Drummond

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