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

Guiver, Chris; Logemann, Hartmut


Hartmut Logemann


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
Keywords Absolute stability, circle criterion, global asymptotic stability, input-to-state stability, Lur’e systems, positive realness, sector-bounded nonlinear operators
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