Robust Asymptotic Stability of Desynchronization in Impulse-Coupled Oscillators
Abstract
The property of desynchronization in an all-to-all network of homogeneous impulse-coupled oscillators is studied. Each impulse-coupled oscillator is modeled as a hybrid system with a single timer state that self-resets to zero when it reaches a threshold, at which event all other impulse-coupled oscillators adjust their timers following a common reset law. In this setting, desynchronization is considered as each impulse-coupled oscillator's timer having equal separation between successive resets. We show that, for the considered model, desynchronization is an asymptotically stable property. For this purpose, we recast desynchronization as a set stabilization problem and employ Lyapunov stability tools for hybrid systems. Furthermore, several perturbations are considered showing that desynchronization is a robust property. Perturbations on both the continuous and discrete dynamics are considered. Numerical results are presented to illustrate the main contributions.
Cite
@article{arxiv.1502.06694,
title = {Robust Asymptotic Stability of Desynchronization in Impulse-Coupled Oscillators},
author = {Sean Phillips and Ricardo G. Sanfelice},
journal= {arXiv preprint arXiv:1502.06694},
year = {2015}
}
Comments
The technical report accompanying "Robust Asymptotic Stability of Desynchronization in Impulse-Coupled Oscillators" to be published in IEEE Transactions on Control of Network Systems, 2015