Incremental input-to-state stability for Lur’e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing

Gilmore, Max; Guiver, Chris; Logemann, Hartmut

Abstract

We prove (integral) input-to-state stability results for a class of forced Lur’e differential inclusions and use them to investigate incremental (integral) input-to-state stability properties of Lur’e differential equations. The latter provide a basis for the derivation of convergence results for trajectories of Lur’e equations generated by Stepanov almost periodic inputs.

Citation

Gilmore, M., Guiver, C., & Logemann, H. (2021). Incremental input-to-state stability for Lur’e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing. Journal of Differential Equations, 300, 692-733. https://doi.org/10.1016/j.jde.2021.08.009

• Journal Article Type: Article
• Acceptance Date: Aug 5, 2021
• Online Publication Date: Aug 19, 2021
• Publication Date: 2021-11
• Deposit Date: Aug 5, 2021
• Publicly Available Date: Aug 20, 2022
• Journal: Journal of Differential Equations
• Print ISSN: 0022-0396
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 300
• Pages: 692-733
• DOI: https://doi.org/10.1016/j.jde.2021.08.009
• Keywords: Absolute stability, almost periodic functions, circle criterion, differential inclusions, incremental (integral) input-to-state stability, (integral) input-to-state stability, Lur’e systems
• Public URL: http://researchrepository.napier.ac.uk/Output/2791584