An operator-theoretic approach to differential positivity

A. Mauroy, F. Forni, R. Sepulchre

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution


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.

Original languageEnglish
Title of host publication54th IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781479978861
Publication statusPublished - 8 Feb 2015
Externally publishedYes
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: 15 Dec 201518 Dec 2015


Conference54th IEEE Conference on Decision and Control, CDC 2015


  • Eigenvalues and eigenfunctions
  • Electrical engineering
  • Limit-cycles
  • Linear systems
  • Manifolds
  • Nonlinear systems
  • Trajectory


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