An operator-theoretic approach to differential positivity

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

Abstract

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.
Pages7028-7033
Number of pages6
ISBN (Electronic)9781479978861
DOIs
Publication statusPublished - 8 Feb 2015
Externally publishedYes
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: 15 Dec 201518 Dec 2015

Conference

Conference54th IEEE Conference on Decision and Control, CDC 2015
CountryJapan
CityOsaka
Period15/12/1518/12/15

Fingerprint

Positive Systems
Linearization
Positivity
Limit Cycle
Cones
Trajectories
Limit Set
Basin of Attraction
Operator
Spectral Properties
Converse
Attractor
Cone
Fixed point
Trajectory
Converge

Keywords

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

Cite this

Mauroy, A., Forni, F., & Sepulchre, R. (2015). An operator-theoretic approach to differential positivity. In 54th IEEE Conference on Decision and Control,CDC 2015 (pp. 7028-7033). [7403327] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7403327
Mauroy, A. ; Forni, F. ; Sepulchre, R. / An operator-theoretic approach to differential positivity. 54th IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 7028-7033
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Mauroy, A, Forni, F & Sepulchre, R 2015, An operator-theoretic approach to differential positivity. in 54th IEEE Conference on Decision and Control,CDC 2015., 7403327, Institute of Electrical and Electronics Engineers Inc., pp. 7028-7033, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 15/12/15. https://doi.org/10.1109/CDC.2015.7403327

An operator-theoretic approach to differential positivity. / Mauroy, A.; Forni, F.; Sepulchre, R.

54th IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 7028-7033 7403327.

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

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KW - Limit-cycles

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Mauroy A, Forni F, Sepulchre R. An operator-theoretic approach to differential positivity. In 54th IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 7028-7033. 7403327 https://doi.org/10.1109/CDC.2015.7403327