Drummond, R. orcid.org/0000-0002-2586-1718, Guiver, C. and Turner, M.C. (2025) A note on incremental stability of externally positive Lurie systems. IEEE Transactions on Automatic Control. ISSN: 0018-9286
Abstract
The Kalman conjecture is shown to be true for Lurie systems in which the linear part is externally positive and the nonlinear element satisfies a generalised incremental gain bound. It is shown further that the system satisfies a range of both traditional and incremental stability properties. Multivariable systems are treated in the same framework as single-input-single output systems, giving the results a wider scope than those normally covered by the Kalman conjecture. Some numerical examples illustrate the utility of the results.
Metadata
| Item Type: | Article |
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| Authors/Creators: |
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| Copyright, Publisher and Additional Information: | © 2025 The Authors. Except as otherwise noted, this author-accepted version of a journal article published in IEEE Transactions on Automatic Control is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Lurie systems; nonlinear systems; robust control; stability of nonlinear systems |
| Dates: |
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| Institution: | The University of Sheffield |
| Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > School of Electrical and Electronic Engineering |
| Date Deposited: | 24 Feb 2026 16:08 |
| Last Modified: | 24 Feb 2026 20:57 |
| Status: | Published |
| Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
| Refereed: | Yes |
| Identification Number: | 10.1109/tac.2025.3615246 |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:238372 |
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Licence: CC-BY 4.0

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