Drummond, R. orcid.org/0000-0002-2586-1718 and Valmorbida, G. orcid.org/0000-0002-1710-8590 (2023) Generalised Lyapunov functions for discrete-time Lurie systems with slope-restricted nonlinearities. IEEE Transactions on Automatic Control. ISSN 0018-9286
Abstract
A class of Lyapunov functions for discrete-time Lurie systems with monotonic non-linearities is proposed. The Lyapunov functions are composed of quadratic terms on the states and of the system's non-linearities as well as Lurie-Postnikov type integral terms. Crucially, positive definiteness of the matrix in the generalised quadratic form and positivity of the scaling terms of the Lurie-Postnikov integrals are relaxed in the stability conditions. Furthermore, they are used for regional stability analysis and performance assessment. Numerical examples show that the proposed Lyapunov function structure matches or outperforms existing ones for these systems.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | Lurie systems; discrete-time absolute stability; Lyapunov functions |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Funding Information: | Funder Grant number ROYAL ACADEMY OF ENGINEERING (THE) ICRF\113 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/P005411/1 ANR ANR-18-CE40-0010 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 29 Mar 2023 13:17 |
Last Modified: | 02 Jan 2024 01:13 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Refereed: | Yes |
Identification Number: | 10.1109/tac.2022.3233540 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:197817 |