A simple extension of contraction theory to study incremental stability properties

Jerome Jouffroy

Research output: Contribution to conference without publisher/journalPaperResearchpeer-review

Abstract

Contraction theory is a recent tool enabling to study the stability of nonlinear systems trajectories with respect to one another, and therefore belongs to the class of incremental stability methods. In this paper, we extend the original definition of contraction theory to incorporate in an explicit manner the control input of the considered system. Such an extension, called universal contraction, is quite analogous in spirit to the well-known Input-to-State Stability (ISS). It serves as a simple formulation of incremental ISS, external stability, and detectability in a differential setting. The hierarchical combination result of contraction theory is restated in this framework, and a differential small-gain theorem is derived from results already available in Lyapunov theory.

Original languageEnglish
Publication date2003
Publication statusPublished - 2003
EventEuropean Control Conference (ECC'03) - Cambridge, United Kingdom
Duration: 24. Aug 2010 → …

Conference

ConferenceEuropean Control Conference (ECC'03)
CountryUnited Kingdom
CityCambridge
Period24/08/2010 → …

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Nonlinear systems
Trajectories

Cite this

Jouffroy, J. (2003). A simple extension of contraction theory to study incremental stability properties. Paper presented at European Control Conference (ECC'03), Cambridge, United Kingdom.
Jouffroy, Jerome. / A simple extension of contraction theory to study incremental stability properties. Paper presented at European Control Conference (ECC'03), Cambridge, United Kingdom.
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Jouffroy, J 2003, 'A simple extension of contraction theory to study incremental stability properties', Paper presented at European Control Conference (ECC'03), Cambridge, United Kingdom, 24/08/2010.

A simple extension of contraction theory to study incremental stability properties. / Jouffroy, Jerome.

2003. Paper presented at European Control Conference (ECC'03), Cambridge, United Kingdom.

Research output: Contribution to conference without publisher/journalPaperResearchpeer-review

TY - CONF

T1 - A simple extension of contraction theory to study incremental stability properties

AU - Jouffroy, Jerome

PY - 2003

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N2 - Contraction theory is a recent tool enabling to study the stability of nonlinear systems trajectories with respect to one another, and therefore belongs to the class of incremental stability methods. In this paper, we extend the original definition of contraction theory to incorporate in an explicit manner the control input of the considered system. Such an extension, called universal contraction, is quite analogous in spirit to the well-known Input-to-State Stability (ISS). It serves as a simple formulation of incremental ISS, external stability, and detectability in a differential setting. The hierarchical combination result of contraction theory is restated in this framework, and a differential small-gain theorem is derived from results already available in Lyapunov theory.

AB - Contraction theory is a recent tool enabling to study the stability of nonlinear systems trajectories with respect to one another, and therefore belongs to the class of incremental stability methods. In this paper, we extend the original definition of contraction theory to incorporate in an explicit manner the control input of the considered system. Such an extension, called universal contraction, is quite analogous in spirit to the well-known Input-to-State Stability (ISS). It serves as a simple formulation of incremental ISS, external stability, and detectability in a differential setting. The hierarchical combination result of contraction theory is restated in this framework, and a differential small-gain theorem is derived from results already available in Lyapunov theory.

M3 - Paper

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Jouffroy J. A simple extension of contraction theory to study incremental stability properties. 2003. Paper presented at European Control Conference (ECC'03), Cambridge, United Kingdom.