A relaxed criterion for contraction theory: application to an underwater vehicle observer

Jerome Jouffroy

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

Abstract

On the contrary to Lyapunov theory, contraction theory studies system behavior independently from a specific attractor, thus leading to simpler computations when verifying exponential convergence of nonlinear systems. To check the contraction property, a condition of negativity on the Jacobian of the system has to be fulfilled. In this paper, attention is paid to results for which the negativity condition can be relaxed, i.e. the maximum eigenvalue of the Jacobian may take zero or positive values. In this issue, we present a theorem and a corollary which sufficient conditions enable to conclude when the Jacobian is not uniformly negative definite but fulfils some weaker conditions. Intended as an illustrative example, a nonlinear underwater vehicle observer, which Jacobian is not uniformly negative definite, is presented and proven to be exponentially convergent using the new criterion.

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 → …

Fingerprint

Nonlinear systems

Keywords

  • contraction theory
  • Exponential convergence
  • nonlinear observers
  • autonomous underwater vehicles

Cite this

Jouffroy, J. (2003). A relaxed criterion for contraction theory: application to an underwater vehicle observer. Paper presented at European Control Conference (ECC'03), Cambridge, United Kingdom.
Jouffroy, Jerome. / A relaxed criterion for contraction theory: application to an underwater vehicle observer. Paper presented at European Control Conference (ECC'03), Cambridge, United Kingdom.
@conference{eb25a2d03dff11dda26c000ea68e967b,
title = "A relaxed criterion for contraction theory: application to an underwater vehicle observer",
abstract = "On the contrary to Lyapunov theory, contraction theory studies system behavior independently from a specific attractor, thus leading to simpler computations when verifying exponential convergence of nonlinear systems. To check the contraction property, a condition of negativity on the Jacobian of the system has to be fulfilled. In this paper, attention is paid to results for which the negativity condition can be relaxed, i.e. the maximum eigenvalue of the Jacobian may take zero or positive values. In this issue, we present a theorem and a corollary which sufficient conditions enable to conclude when the Jacobian is not uniformly negative definite but fulfils some weaker conditions. Intended as an illustrative example, a nonlinear underwater vehicle observer, which Jacobian is not uniformly negative definite, is presented and proven to be exponentially convergent using the new criterion.",
keywords = "contraction theory, Exponential convergence, nonlinear observers, autonomous underwater vehicles",
author = "Jerome Jouffroy",
year = "2003",
language = "English",
note = "null ; Conference date: 24-08-2010",

}

Jouffroy, J 2003, 'A relaxed criterion for contraction theory: application to an underwater vehicle observer', Paper presented at European Control Conference (ECC'03), Cambridge, United Kingdom, 24/08/2010.

A relaxed criterion for contraction theory: application to an underwater vehicle observer. / 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 relaxed criterion for contraction theory: application to an underwater vehicle observer

AU - Jouffroy, Jerome

PY - 2003

Y1 - 2003

N2 - On the contrary to Lyapunov theory, contraction theory studies system behavior independently from a specific attractor, thus leading to simpler computations when verifying exponential convergence of nonlinear systems. To check the contraction property, a condition of negativity on the Jacobian of the system has to be fulfilled. In this paper, attention is paid to results for which the negativity condition can be relaxed, i.e. the maximum eigenvalue of the Jacobian may take zero or positive values. In this issue, we present a theorem and a corollary which sufficient conditions enable to conclude when the Jacobian is not uniformly negative definite but fulfils some weaker conditions. Intended as an illustrative example, a nonlinear underwater vehicle observer, which Jacobian is not uniformly negative definite, is presented and proven to be exponentially convergent using the new criterion.

AB - On the contrary to Lyapunov theory, contraction theory studies system behavior independently from a specific attractor, thus leading to simpler computations when verifying exponential convergence of nonlinear systems. To check the contraction property, a condition of negativity on the Jacobian of the system has to be fulfilled. In this paper, attention is paid to results for which the negativity condition can be relaxed, i.e. the maximum eigenvalue of the Jacobian may take zero or positive values. In this issue, we present a theorem and a corollary which sufficient conditions enable to conclude when the Jacobian is not uniformly negative definite but fulfils some weaker conditions. Intended as an illustrative example, a nonlinear underwater vehicle observer, which Jacobian is not uniformly negative definite, is presented and proven to be exponentially convergent using the new criterion.

KW - contraction theory

KW - Exponential convergence

KW - nonlinear observers

KW - autonomous underwater vehicles

M3 - Paper

ER -

Jouffroy J. A relaxed criterion for contraction theory: application to an underwater vehicle observer. 2003. Paper presented at European Control Conference (ECC'03), Cambridge, United Kingdom.