The Circle Criterion and Input-to-State Stability

Author

Jayawardhana, Bayu ; Logemann, Hartmut ; Ryan, Eugene P.

Volume

31

Issue

4

fYear

2011

Firstpage

32

Lastpage

67

Abstract

This article provides an overview of the circle criterion and its connection with ISS. Classical absolute stability theory and the circle criterion in particular, is concerned with the analysis of a feedback interconnection of Lure type, which consists of a linear system in the forward path and a sector-bounded nonlinearity in the negative feedback path. Classical absolute stability results are revis ited in the context of systems described by differential inclusions and within a framework based on the complex Aizerman conjecture. Contrast with the classical literature that is focused mainly on asymptotic stability of the feedback interconnection, ISS issues are addressed and resolved.

Keywords

absolute stability; asymptotic stability; control nonlinearities; feedback; linear systems; ISS issue; Lure type; absolute stability theory; asymptotic stability; complex Aizerman conjecture; differential inclusion; feedback interconnection; input-to-state stability; linear system; negative feedback path; sector bounded nonlinearity; Feedback control; Interconnected systems; Linear systems; Stability analysis; State feedback;

fLanguage

English

Journal_Title

Control Systems, IEEE

Publisher

ieee

ISSN

1066-033X

Type

jour

DOI

10.1109/MCS.2011.941143

Filename

5942955