On the consensus of homogeneous multi-agent systems with arbitrarily switching topology

In this paper we investigate the consensus problem under arbitrary switching for homogeneous multi-agent systems with switching communication topology, by assuming that each agent is described by a single-input stabilizable state–space model and that the communication graph is connected at every time instant. Under these assumptions, we construct a common quadratic positive definite Lyapunov function for the switched system describing the evolution of the disagreement vector, thus showing that the agents always reach consensus. In addition, the proof leads to the explicit construction of a constant state-feedback matrix that allows the multi-agent system to achieve consensus.