Structural properties of multi-agent linear systems with applications to leader-following consensus

The controllability and observability of leader-following multi-agent linear systems under switching topology are considered. Unlike the existing results, the controllability and observability are analyzed in a different context. More specifically, as for the controllability problem, the admissible control input for each follower agent can only use relative and local information from its neighbors and the control objective is the convergence of each follower´s state to to that of the leader agent; as for the observability problem, the output of the multi-agent systems is all the information transmitted in the multi-agent network. It turns out that under the controllability and observability of individual system, the jointly connected switching topology, including fixed topology as a special case, implies the controllability and observability of the multi-agent systems. As applications, these properties are used in the leader-following consensus problem under switching topology.