State consensus for homogeneous multi-agent systems over time-varying undirected graph

Abstract

We investigate state consensus for homogeneous multi-agent systems (MASs) over time-varying undirected graphs. Different from the existing literature, we consider the use of static state feedback protocols over time-varying graphs that involve both switches, and continuous variations. Using the known results from the system theory, we are able to derive the necessary and sufficient condition for state consensus that requires the time-varying graph to be uniformly connected, and the observability of the persistent modes over the time-varying graph, which is shown to hold if the time-varying graph involves only switches, and is true generically for more general piecewise continuous time-varying graphs. A numerical example is worked out to illustrate our consensus results.