@article {112, title = {Robust Asymptotic Stability of Desynchronization in Impulse-Coupled Oscillators}, journal = {IEEE Transactions on Control of Network Systems}, volume = {3}, year = {2016}, month = {June}, pages = {127-136}, 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{\textquoteright}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.

}, keywords = {hybrid systems}, author = {S. Phillips and R. G. Sanfelice} } @conference {102, title = {Results on Incremental Stability for a Class of Hybrid Systems}, booktitle = {Proceedings of the 53rd IEEE Conference on Decision and Control}, series = {NULL}, year = {2014}, month = {December}, pages = {3089--3094}, abstract = {

Incremental stability is the notion that the distance between every pair of solutions to the system has stable behavior and approaches zero asymptotically. This paper introduces this notion for a class of hybrid systems. In particular, we define incremental stability as well as incremental partial stability, and study their properties. The approach used to derive our results consists of recasting the incremental stability problem as a set stabilization problem, for which the tools for asymptotic stability of hybrid systems are applicable. In particular, we propose an auxiliary hybrid system to study the stability of the diagonal set, which relates to incremental stability of the original system. The proposed notions are illustrated in examples throughout the paper.

}, keywords = {hybrid systems}, author = {Y. Li and S. Phillips and R. G. Sanfelice} } @conference {93, title = {A Framework for Modeling and Analysis of Robust Stability for Spiking Neurons}, booktitle = {Proceedings of the American Control Conference}, series = {NULL}, year = {2014}, month = {June}, pages = {1414-1419}, keywords = {hybrid systems}, author = {S. Phillips and R. G. Sanfelice} } @conference {72, title = {Results on the Asymptotic Stability Properties of Desynchronization in Impulse-coupled Oscillators}, booktitle = {Proceedings of the American Control Conference}, series = {NULL}, year = {2013}, month = {June}, pages = {3278{\textendash}3283}, keywords = {hybrid systems}, url = {https://hybrid.soe.ucsc.edu/files/preprints/72.pdf}, author = {S. Phillips and R. G. Sanfelice} } @conference {61, title = {On the Synchronization of Two Impulsive Oscillators under Communication Constraints}, booktitle = {Proceedings of the American Control Conference}, series = {NULL}, year = {2012}, pages = {2443{\textendash}2448}, keywords = {hybrid systems}, doi = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=\&arnumber=6315647}, url = {https://hybrid.soe.ucsc.edu/files/preprints/61.pdf}, author = {S. Phillips and R. G. Sanfelice and R. S. Erwin} }