The Circle Criterion and Input-to-State Stability

New perspectives on a classical result

Research output: Contribution to journalArticle

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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.
Original languageEnglish
Pages (from-to)32-67
Number of pages36
JournalIEEE Control Systems Magazine
Volume31
Issue number4
DOIs
Publication statusPublished - Aug 2011

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Absolute Stability
Interconnection
Circle
Feedback
Path
Negative Feedback
Stability Theory
Differential Inclusions
Asymptotic Stability
Sector
Linear Systems
Nonlinearity
Asymptotic stability
Linear systems
Context
Framework

Cite this

The Circle Criterion and Input-to-State Stability : New perspectives on a classical result. / Jayawardhana, B; Logemann, Hartmut; Ryan, Eugene P.

In: IEEE Control Systems Magazine, Vol. 31, No. 4, 08.2011, p. 32-67.

Research output: Contribution to journalArticle

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