Details

Autor(en) / Beteiligte

• Mauroy, A.
• Forni, F.
• Sepulchre, R.

Titel

An operator-theoretic approach to differential positivity

Ist Teil von

• 2015 54th IEEE Conference on Decision and Control (CDC), 2015, p.7028-7033

Ort / Verlag

IEEE

Erscheinungsjahr

2015

Quelle

IEL

Beschreibungen/Notizen

• 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.