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

J. Jouffroy

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Abstract

On the contrary to Lyapunov theory, contraction theory studiessystem behavior independently from a specific attractor, thusleading to simpler computations when verifying exponentialconvergence of nonlinear systems. To check the contractionproperty, a condition of negativity on the Jacobian of the sys-tem has to be fulfilled. In this paper, attention is paid to resultsfor which the negativity condition can be relaxed,i.e.the max-imum eigenvalue of the Jacobian may take zero or positive val-ues. In this issue, we present a theorem and a corollary whichsufficient conditions enable to conclude when the Jacobian isnot uniformly negative definite but fulfils some weaker condi-tions. Intended as an illustrative example, a nonlinear underwa-ter vehicle observer, which Jacobian is not uniformly negativedefinite, is presented and proven to be exponentially convergentusing the new criterion.
OriginalsprogEngelsk
TitelEuropean Control Conference, ECC 2003
Publikationsdato2003
StatusUdgivet - 2003
Udgivet eksterntJa

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  • Teknik, ingeniørvidenskab og IT

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