An operator-theoretic approach to differential positivity
2015 54th IEEE Conference on Decision and Control (CDC)
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Mauroy, A., Forni, F., & Sepulchre, R. (2015). An operator-theoretic approach to differential positivity. 2015 54th IEEE Conference on Decision and Control (CDC), 7028-7033. https://doi.org/10.1109/CDC.2015.7403327
Differentially positive systems are systems whose linearization along trajectories is positive. Under mild assumptions, their solutions asymptotically converge to a onedimensional 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.
A. Mauroy holds a BELSPO Return Grant and F. Forni holds a FNRS fellowship. This paper presents research results of the Belgian Network DYSCO, funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office.
External DOI: https://doi.org/10.1109/CDC.2015.7403327
This record's URL: https://www.repository.cam.ac.uk/handle/1810/251264