The problem of synchronization of multiple linear time-invariant systems connected over a network with asynchronous and intermittently available communication events is studied. To solve this problem, we propose a controller with hybrid dynamics, namely, the controller utilizes information transmitted to it during discrete communication events and exhibits continuous dynamics between such events. Due to the additional continuous and discrete dynamics inherent to the interconnected networked systems and communication structure, we use a hybrid systems framework to model and analyze the closed-loop system. The problem of synchronization is then recast as a set stabilization problem and, by employing Lyapunov stability tools for hybrid systems, sufficient conditions for asymptotic stability of the synchronization set are provided. Furthermore, we show that the property of synchronization is robust to perturbations. Numerical examples illustrating the main results are included. (C) 2019 Elsevier B.V. All rights reserved.