An operator-theoretic approach to differential positivity

A. Mauroy, F. Forni, R. Sepulchre

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Differentially positive systems are systems whose linearization along trajectories is positive. Under mild assumptions, their solutions asymptotically converge to a one-dimensional attractor, which must be a limit cycle in the absence of fixed points in the limit set. In this paper, we investigate the general connections between the (geometric) properties of differentially positive systems and the (spectral) properties of the Koopman operator. In particular, we obtain converse results for differential positivity, showing for instance that any hyperbolic limit cycle is differentially positive in its basin of attraction. We also provide the construction of a contracting cone field.

langue originaleAnglais
titre54th IEEE Conference on Decision and Control,CDC 2015
EditeurInstitute of Electrical and Electronics Engineers Inc.
Nombre de pages6
ISBN (Electronique)9781479978861
Les DOIs
Etat de la publicationPublié - 8 févr. 2015
Modification externeOui
Evénement54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japon
Durée: 15 déc. 201518 déc. 2015

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Une conférence54th IEEE Conference on Decision and Control, CDC 2015
La villeOsaka

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