Pointwise Exponential Stability of State Consensus with Intermittent Communication

In this paper, we propose a solution to the problem of achieving global consensus of the states of scalar integrator systems over a directed graph when the network connecting the agents is available only at isolated (and possibly aperiodic) time instances. We propose decentralized consensus protocols that, using such intermittent information obtained at communication times, globally and asymptotically drives the values of their states to an agreement value, with stability and robustness to perturbations on the dynamics, the information exchanged over the network, and the communication times. Using stability analysis tools for hybrid systems, we recast the consensus problem as a set stabilization problem and leverage Lyapunov stability tools for the analysis of the networked system, both in the nominal and perturbed cases. When communication between the agents occurs synchronously, we show that the set of points characterizing consensus is globally exponentially stable, and, under some mild additional conditions, is partially pointwise globally exponentially stable. On the other hand, when communication occurs asynchronously, we show global asymptotic stability of consensus, for which we exploit well-posedness of the hybrid system modeling the network and an hybrid invariance principle. Results certifying robustness of the proposed consensus protocols, to a wide class of perturbations, are presented. Numerical examples illustrate the main results.