Synchronization Reachable Topology and Synchronization of Discrete-Time Linear Multi-Agent Systems

In this note, we consider the synchronization problem for discrete-time linear multi-agent systems with time-varying network topology. To describe a new joint connectivity condition for synchronization, the concept of synchronization reachable topology is introduced. Under the conditions that agent dynamics is neutrally stable and network topology is synchronization reachable, a synchronization and an exponential synchronization result are obtained using paracontraction theory. The two results generalize in a natural way the classical results for the consensus of first-order discrete-time multi-agent systems. Finally, the effectiveness of the results is illustrated by a simulation example.