  We study convergence in networks of piecewise-smooth (PWS) systems that
commonly arise in applications to model dynamical systems whose evolution is
affected by macroscopic events such as switches and impacts. Existing
approaches were typically oriented toward guaranteeing global bounded
synchronizability, local stability of the synchronization manifold, or
achieving synchronization by exerting a control action on each node. Here we
start by generalizing existing results on QUAD systems to the case of PWS
systems, accounting for a large variety of nonlinear coupling laws. Then, we
propose that a discontinuous coupling can be used to guarantee global
synchronizability of a network of N PWS agents under mild assumptions on the
individual dynamics. We provide extensive numerical simulations to gain
insights on larger networks.
