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An operator-theoretic approach to differential positivity

Mauroy, A and Forni, F and Sepulchre, R (2015) An operator-theoretic approach to differential positivity. In: UNSPECIFIED pp. 7028-7033..

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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.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Divisions: Div F > Control
Depositing User: Unnamed user with email
Date Deposited: 17 Jul 2017 19:19
Last Modified: 09 Sep 2021 03:04
DOI: 10.1109/CDC.2015.7403327