Continuous-time consensus with discrete-time communication

This paper describes a solution to a consensus problem whereby a group of agents evolve in continuous-time and exchange information at discrete instants of times. In the setup adopted each agent is viewed as a node in a graph, its evolution is represented by a scalar node variable, and all agents seek to agree on a common value. The agents are allowed to exchange information among each other but only at specified update times. The topology of the communication network can change over time and the information received by one agent from a subset of the other agents may be outdated. The solution proposed relies on the introduction of an extra variable for each agent that is updated instantaneously at update times. In between updates, both the node and the extra variables evolve in a continuous fashion. The proof that consensus is achieved is done by reducing the system under study to a discrete-time equivalent one and resorting to results on consensus for discrete-time systems.