UC Santa Cruz

The property of synchronization of multiple linear time-invariant systems connected over a network with stochastically-driven isolated communication events is studied. We propose a solution to the problem of designing a feedback controller that, using information obtained over such networks, asymptotically drives the values of their states to synchronization and renders such a condition Lyapunov stable. To solve this problem, we propose a controller with hybrid dynamics, namely, the controller exhibits continuous dynamics between communication events and, at such events, has variables that jump. 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 the synchronization property is robust to a class of perturbations on the transmitted data. Numerical examples illustrating the main results are included.