Connections between finite-gain and asymptotic stability

David J. Hill; Peter J. Moylan

doi:10.1109/TAC.1980.1102463

Connections between finite-gain and asymptotic stability

David J. Hill
, Peter J. Moylan

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

160 Citations (Scopus)

Abstract

The relationship between input-output and Lyapunov stability properties for nonlinear systems is studied. Well-known definitions for the input-output properties of finite-gain and passivity, even with quite reasonable minimality assumptions on a state-space representation, do not necessarily imply any form of stability for the state. Attention is given to the precise versions of input-output and observability properties which guarantee asymptotic stability. Particular emphasis is given to the possibility of multiple equilibria for the dynamical system.

Original language	English
Pages (from-to)	931-936
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	25
Issue number	5
DOIs	https://doi.org/10.1109/TAC.1980.1102463
Publication status	Published - Oct 1980
Externally published	Yes

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10.1109/TAC.1980.1102463

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title = "Connections between finite-gain and asymptotic stability",

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AB - The relationship between input-output and Lyapunov stability properties for nonlinear systems is studied. Well-known definitions for the input-output properties of finite-gain and passivity, even with quite reasonable minimality assumptions on a state-space representation, do not necessarily imply any form of stability for the state. Attention is given to the precise versions of input-output and observability properties which guarantee asymptotic stability. Particular emphasis is given to the possibility of multiple equilibria for the dynamical system.

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Connections between finite-gain and asymptotic stability

Abstract

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