Stability of Forced Higher-Order Continuous-Time Lur'e Systems: a Behavioural Input-Output Perspective

Guiver, Chris; Logemann, Hartmut

Abstract

We consider a class of forced continuous-time Lur'e systems obtained by applying nonlinear feedback to a higher-order linear differential equation which defines an input-output system in the sense of behavioural systems theory. This linear system directly relates the input and output signals and does not involve any internal, latent or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability and strong integral input-to-output stability, concepts which are very much reminiscent of input-to-state stability and strong integral input-to-state stability, respectively. The methods used in the paper combine ideas from the behavioural approach to systems and control, absolute stability theory and input-to-state stability theory.

Citation

Guiver, C., & Logemann, H. (2024). Stability of Forced Higher-Order Continuous-Time Lur'e Systems: a Behavioural Input-Output Perspective. International Journal of Control, 97(8), 1788-1809. https://doi.org/10.1080/00207179.2023.2233023

• Journal Article Type: Article
• Acceptance Date: Jun 28, 2023
• Online Publication Date: Aug 4, 2023
• Publication Date: 2024
• Deposit Date: Jun 28, 2023
• Publicly Available Date: Aug 4, 2023
• Print ISSN: 0020-7179
• Electronic ISSN: 1366-5820
• Publisher: Taylor & Francis
• Peer Reviewed: Peer Reviewed
• Volume: 97
• Issue: 8
• Pages: 1788-1809
• DOI: https://doi.org/10.1080/00207179.2023.2233023
• Keywords: Absolute stability, behaviours, circle criterion, forced higher-order differential equations, input-to-output stability, Lur'e systems
• Publisher URL: https://www.tandfonline.com/journals/tcon20