Leaderless synchronization of linear multi-agent systems under directed switching topologies: An invariance approach

In this paper, we study the synchronization problem for a class of identical linear, high order systems. The interconnections between the systems are assumed to be time-varying, directed, and the underlying graph is not necessarily connected at any time instant. We show that in this setup, even destabilization may occur through diffusive couplings. In order to overcome this problem, we present a distributed control law, which is able to guarantee positive invariance of energy level-sets, and we investigate its synchronizing properties.