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For asymptotically periodic systems, a powerful (phase) reduction of the dynamics is obtained by computing the so-called isochrons, i.e. the sets of points that converge toward the same trajectory onâ€¦ (More)

- Alexandre Mauroy, Igor Mezic
- IEEE Transactions on Automatic Control
- 2016

We propose a novel operator-theoretic framework to study global stability of nonlinear systems. Based on the spectral properties of the so-called Koopman operator, our approach can be regarded as aâ€¦ (More)

- Alexandre Mauroy, Igor Mezic
- Chaos
- 2012

The concept of isochrons is crucial for the analysis of asymptotically periodic systems. Roughly, isochrons are sets of points that partition the basin of attraction of a limit cycle according to theâ€¦ (More)

- Alexandre Mauroy, Pierre SacrÃ©, Rodolphe Sepulchre
- 2012 IEEE 51st IEEE Conference on Decision andâ€¦
- 2012

The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature onâ€¦ (More)

- Alexandre Mauroy, Rodolphe Sepulchre
- IEEE Transactions on Automatic Control
- 2013

We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupled models, the stabilityâ€¦ (More)

- Alexandre Mauroy, Igor Mezic
- 52nd IEEE Conference on Decision and Control
- 2013

The global description of a nonlinear system through the linear Koopman operator leads to an efficient approach to global stability analysis. In the context of stability analysis, not much attentionâ€¦ (More)

- Alexandre Mauroy, Jorge Goncalves
- 2016 IEEE 55th Conference on Decision and Controlâ€¦
- 2016

We exploit the key idea that nonlinear system identification is equivalent to linear identification of the so-called Koopman operator. Instead of considering nonlinear system identification in theâ€¦ (More)

- Alexandre Mauroy, Rodolphe Sepulchre
- Systems & Control Letters
- 2012

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance.â€¦ (More)

- Aivar Sootla, Alexandre Mauroy
- ArXiv
- 2015

In this paper, we consider the systems with trajectories originating in the nonnegative orthant becoming nonnegative after some finite time transient. First we consider dynamical systems (i.e., fullyâ€¦ (More)

- Aivar Sootla, Alexandre Mauroy
- IEEE Control Systems Letters
- 2018

Eventually monotone systems are dynamical systems whose solutions preserve a partial order in the initial condition after some initial transient. While monotone systems have a characterization inâ€¦ (More)