Leader-follower consensus of multi-agent systems

This paper addresses the leader-follower consensus problem of multi-agent systems with a time-invariant communication topology consisting of general linear node dynamics. A distributed observer-type consensus protocol based on relative output measurements is proposed. It is shown that the leader-follower consensus of multi-agent systems can be cast equivalently into the stability of a set of matrices of the same dimension as a single agent. The notion of consensus region is then introduced and analyzed by using tools from the stability of matrix pencils. It is further demonstrated that there exists an observer-type protocol that solves the leader-follower consensus problem, and meanwhile yields an unbounded consensus region, if and only if the agent dynamics are stabilizable and detectable. A multi-step consensus protocol design procedure is finally presented. The effectiveness of the theoretical results is demonstrated through numerical simulations.