Robust Synchronization of Interconnected Linear Systems over Intermittent Communication Networks

The property of synchronization of multiple identical linear time-invariant (LTI) systems connected through a graph in a network with stochastically-driven isolated communication events is studied. More precisely, the goal is to design a feedback controller that, using information obtained over such networks, asymptotically drives the values of their states to synchronization and render the synchronization condition Lyapunov stable. To solve this problem, we propose a controller with hybrid dynamics, namely, the controller exhibits continuous dynamics between communication events while it has variables that jump at such events. Due to the additional continuous and discrete dynamics inherent to the networked systems and communication structure, we use a hybrid systems framework to model the closed-loop system and design the controller. The problem of synchronization is then recast as a compact 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 synchronization property is robust to a class of perturbations on the transmitted data. Numerical examples illustrate the main results.