Robust Asymptotic Stability of Desynchronization in Impulse-Coupled Oscillators

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D. Journal Articles


IEEE Transactions on Control of Network Systems, Volume 3, Issue 2, p.127-136 (2016)

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hybrid systems


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 the continuous and discrete dynamics are considered. Numerical results are presented to illustrate the main contributions.


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