Uniform global asymptotic synchronization of Kuramoto oscillators via hybrid coupling

Abstract

Using a hybrid framework, we propose a generalized version of the well-known Kuramoto model for interconnected oscillators. The proposed model does not modify the classical model close to the synchronization set, but avoids the typical non-uniform convergence phenomenon. For the two-oscillators case, we prove the uniform global asymptotic stability of the consensus set by using a hybrid Lyapunov function whose generality promises possible extension of the result to higher order dynamics. We comparatively illustrate the achieved uniform convergence properties by simulating both the case with two and multiple oscillators, thus confirming the effectiveness of our approach.