Passivity theorems for input-to-state stability of forced Lur’e inclusions and equations, and consequent entrainment-type properties

Guiver, Chris

Abstract

A suite of input-to-state stability results are presented for a class of forced differential inclusions, so-called Lur’e inclusions. As a consequence, semi-global incremental input-to-state stability results for systems of forced Lur’e differential equations are derived. The results are in the spirit of the passivity theorem from control theory as both the linear and nonlinear components of the Lur’e inclusion (or equation) are assumed to satisfy passivity-type conditions. These results provide a basis for the analysis of forced Lur’e differential equations subject to (almost) periodic forcing terms and, roughly speaking, ensure the existence and attractivity of (almost) periodic state- and output-responses, comprising another focus of the present work. One ultimate aim of the study is to provide a robust and rigorous theoretical foundation for a well-defined and tractable “frequency response” of forced Lur’e systems.

Citation

Guiver, C. (2025). Passivity theorems for input-to-state stability of forced Lur’e inclusions and equations, and consequent entrainment-type properties. ESAIM: Control, Optimisation and Calculus of Variations, 31, Article 22. https://doi.org/10.1051/cocv/2025013

• Journal Article Type: Article
• Acceptance Date: Jan 20, 2025
• Online Publication Date: Mar 20, 2025
• Publication Date: 2025
• Deposit Date: Jan 24, 2025
• Publicly Available Date: Mar 20, 2025
• Journal: ESAIM: Control, Optimisation and Calculus of Variations
• Print ISSN: 1292-8119
• Electronic ISSN: 1262-3377
• Publisher: EDP Sciences
• Peer Reviewed: Peer Reviewed
• Volume: 31
• Article Number: 22
• DOI: https://doi.org/10.1051/cocv/2025013
• Keywords: Almost periodic function, differential inclusion, entrainment, incremental stability, input-to-state stability, Lur’e system
• Public URL: http://researchrepository.napier.ac.uk/Output/4056126
• Publisher URL: https://www.esaim-cocv.org/