About disconnected topology and cluster consensus∗

In this paper we analyze the problem of consensus of homogeneous nonlinear agents in case of disconnected topology. Specifically, we look for diffusive coupling strategies able to enforce the so-called cluster consensus within the networked agents. In order to avoid instability of a certain group of agents (referred to as residual agents) not belonging to connected components, we modify the conventional diffuse coupling by means of a time dependent strategy clustering the graph in the minimum number of connected components within which all the agents reach a consensus. Suficient conditions for achieving cluster consensus are obtained by means of Lyapunov tools. Simulation results are also presented.