Stability of nonlinear feedback systems: A new small-gain theorem

Anna L. Chen; Gui Qiang Chen; Randy A Freeman

doi:10.1137/S0363012904440812

Stability of nonlinear feedback systems: A new small-gain theorem

Anna L. Chen, Gui Qiang Chen, Randy A Freeman

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

For the feedback interconnection of general nonlinear systems, the classical small-gain condition is sufficient but not necessary for robust stability. We introduce a weaker notion of gain which yields a small-gain condition that is both necessary and sufficient for robust stability. We also discuss conditions under which the two notions coincide, and we further provide results for dissipation performance measures that are more general than the classical gain measures.

Original language	English (US)
Pages (from-to)	1995-2012
Number of pages	18
Journal	SIAM Journal on Control and Optimization
Volume	46
Issue number	6
DOIs	https://doi.org/10.1137/S0363012904440812
State	Published - Dec 1 2007

Keywords

Conditional gain
Dissipativity
Feedback connection
Nonlinear systems
Performance analysis
Small-gain theorem

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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AU - Chen, Gui Qiang

AU - Freeman, Randy A

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N2 - For the feedback interconnection of general nonlinear systems, the classical small-gain condition is sufficient but not necessary for robust stability. We introduce a weaker notion of gain which yields a small-gain condition that is both necessary and sufficient for robust stability. We also discuss conditions under which the two notions coincide, and we further provide results for dissipation performance measures that are more general than the classical gain measures.

AB - For the feedback interconnection of general nonlinear systems, the classical small-gain condition is sufficient but not necessary for robust stability. We introduce a weaker notion of gain which yields a small-gain condition that is both necessary and sufficient for robust stability. We also discuss conditions under which the two notions coincide, and we further provide results for dissipation performance measures that are more general than the classical gain measures.

KW - Conditional gain

KW - Dissipativity

KW - Feedback connection

KW - Nonlinear systems

KW - Performance analysis

KW - Small-gain theorem

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