for sensor networks [@Liu05adynamic].

Motivated by the applications mentioned above and the lack of a full understanding of desynchronization in multi-agent systems, this paper pertains to the study of the dynamical properties of desynchronization in a network of impulse-coupled oscillators with an all-to-all communication graph. The uniqueness of the approach emerges from the use of hybrid systems tools, which not only conveniently capture the continuous and impulsive behavior in the networks of interest, but also are suitable for analytical study of asymptotic stability and robustness to perturbations.

More precisely, the dynamics of the proposed hybrid system capture the (linear) continuous evolution of the states as well their impulsive/discontinuous behavior due to state triggered events. Analysis of the asymptotic behavior of the trajectories (or solutions) to these systems is performed using the framework of hybrid systems introduced in [@teel2012hybrid; @Goebel.ea.09.CSM]. To this end, we recast the study of desynchronization as a set stabilization problem. Unlike synchronization, for which the set of points to stabilize is obvious, the complexity of desynchronization requires first to determine such a collection of points, which we refer to as the [*desynchronization set*]{}. We propose an algorithm to compute such set of points. Then, using Lyapunov stability 