Exponential input-to-state stability for Lur’e systems via Integral Quadratic Constraints and Zames-Falb Multipliers

Drummond, Ross; Guiver, Chris; Turner, Matthew

Abstract

Absolute stability criteria which are sufficient for global exponential stability are shown, under a Lipschitz assumption, to be sufficient for the a priori stronger exponential input-to-state stability property. Important corollaries of this result are: i) absolute stability results obtained using Zames-Falb multipliers for systems containing slope-restricted nonlinearities provide exponential input-to-state-stability under a mild detectability assumption; and ii) more generally, many absolute stability results obtained via integral quadratic constraint (IQC) methods provide, with the additional Lipschitz assumption, this stronger property.

Citation

Drummond, R., Guiver, C., & Turner, M. (2024). Exponential input-to-state stability for Lur’e systems via Integral Quadratic Constraints and Zames-Falb Multipliers. IMA Journal of Mathematical Control and Information, 41(1), 1-17. https://doi.org/10.1093/imamci/dnae003

• Journal Article Type: Article
• Acceptance Date: Dec 30, 2023
• Online Publication Date: Feb 4, 2024
• Publication Date: 2024-03
• Deposit Date: Jan 5, 2024
• Publicly Available Date: Feb 5, 2025
• Print ISSN: 0265-0754
• Electronic ISSN: 1471-6887
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 41
• Issue: 1
• Pages: 1-17
• DOI: https://doi.org/10.1093/imamci/dnae003
• Keywords: absolute stability, exponential input-to-state stability, Integral Quadratic Constraint, Lur’e system, Zames-Falb multiplier
• Public URL: http://researchrepository.napier.ac.uk/Output/3446024
• Publisher URL: https://academic.oup.com/imamci