A Hybrid Consensus Protocol for Pointwise Exponential Stability with Intermittent Information

We propose a solution to the problem of achieving consensus of the state of multiple systems connected over a network (over a directed graph) in which communication events are triggered stochastically. Our solution consists of a protocol design that, using intermittent information obtained over the network, asymptotically drive the values of their states to agreement, with stability, globally and with robustness to perturbations. More precisely, we propose a protocol with hybrid dynamics, namely, an algorithm with variables that jump at the communication events and evolve continuously in between such events. We design the protocols by recasting the consensus problem as a set stabilization problem and applying Lyapunov stability tools for hybrid systems. We provide sufficient conditions for exponential stability of the consensus set. Furthermore, we show that under additional conditions this set is also partially pointwise globally exponentially stable. Robustness of consensus to certain classes of perturbations is also established. Numerical examples confirm the main results.