Coordination of Linear Systems with Finite Data Rate and Time-Varying Undirected Topologies

This paper focuses on the synchronization of discrete-time linear multi-agent systems with finite communication data rate and switching undirected topology flows. Quantizedobserver based communication schemes and adaptive encoder-decoders are proposed. We show that there exist such protocols leading to synchronization exponentially fast with only finite bits of information exchanged per step, if the agents' dynamics satisfies some simultaneously stabilizable conditions and network topology flows are frequently connected. For first-order dynamics, the number of bits are related to the unstable mode of agent dynamics, the number of agents, the frequency of connectivity and the Laplacian eigenvalue ratio of the switching topology flow.