The circle criterion for a class of sector-bounded dynamic nonlinearities

Guiver, Chris; Logemann, Hartmut

Abstract

We present a circle criterion which is necessary and sufficient for absolute stability with respect to a natural class of sector-bounded nonlinear causal operators. This generalized circle criterion contains the classical result as a special case. Furthermore, we develop a version of the generalized criterion which guarantees input-to-state stability.

• Journal Article Type: Article
• Acceptance Date: Mar 16, 2022
• Online Publication Date: Apr 18, 2022
• Publication Date: 2022-09
• Deposit Date: Mar 17, 2022
• Publicly Available Date: Apr 19, 2023
• Journal: Mathematics of Control, Signals, and Systems
• Print ISSN: 0932-4194
• Electronic ISSN: 1435-568X
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Pages: 461-492
• DOI: https://doi.org/10.1007/s00498-022-00324-3
• Keywords: Absolute stability, circle criterion, global asymptotic stability, input-to-state stability, Lur’e systems, positive realness, sector-bounded nonlinear operators
• Public URL: http://researchrepository.napier.ac.uk/Output/2855351