Consensus controllability, observability and robust design for leader-following linear multi-agent systems

This paper considers, for leader-following linear multi-agent systems (MAS) connected by switching graphs, the consensus controllability and observability, and extends the existing results which are valid only for fixed graph case. Unlike the general controllability and observability problems which require each state to be controllable and observable, we only examine the consensus state to be controllable and the tracking error states between the followers and the leader to be observable. As for the consensus controllability, the admissible control input for each follower agent can only obtain relative and local information from its neighbors, and the control objective is to render the MAS to achieve consensus, in the sense of convergence of each follower's state to that of a leader agent. As for the consensus observability, the output of the MAS is the information-flow in the multi-agent network, and the observation task is to reconstruct the tracking error states between the followers and the leader. It is demonstrated in this paper that the controllability and observability of each individual system and the jointly connected switching topology (including fixed topology as a special case) jointly imply the consensus controllability and observability of the MAS. The consensus controllability property is used in the robust leader-following consensus problem, and the consensus observability property is used in the robust observer-based leader-following consensus problem, both under switching topology.