On the stability and robustness of Stuart-Landau oscillators

Elena Panteley (1, 2) , Antonio Loria (1) , Ali El Ati (1)

1 L2S - Laboratoire des signaux et systèmes
2 Saint Petersburg State University of Information Technologies Mechanics and Optics

e study of oscillations, from a dynamical-systems-theory viewpoint is a subject of interest in a variety of research domains ranging from physical sciences to engineering. One of the main motivations to study the behaviour of solutions of these complex systems lies in their role in modelling of collective behaviour, such as synchrony, which appears naturally in some biological systems but also in technological creations such as power grids. In particular, Stuart-Landau oscillators are used to model the so-called Andronov bifurcation, from oue equilibrium to a limit cycle. In this paper, we employ modern tools of stability theory to analyse the behaviour of solutions of Stuart-Landau forced and unforced oscillators. We establish su cient conditions for global asymptotic and input-to-state stability with respect to sets.

Mots clés: Synchronisation; oscillations; nonlinear systems; robust stability

Domaines: Automatique / Robotique

Elena Panteley, Antonio Loria, Ali El Ati. On the stability and robustness of Stuart-Landau oscillators. 1st IFAC Conference on Modelling, Identification and Control of Nonlinear Systems (MICNON), Jun 2015, St. Petersbourg, Russia. pp.645-650, ⟨10.1016/j.ifacol.2015.09.260⟩. ⟨hal-01262570⟩