Bipartite Tracking Consensus of Linear Multi-Agent Systems with a Dynamic Leader

In this brief, the distributed bipartite tracking consensus problem for linear multi-agent systems (MASs) in the presence of a single leader is investigated. Compared with some related works on this topic, the leader's control inputs in the present MAS model are allowed to be nonzero and unknown to each follower. To guarantee bipartite tracking consensus, a new kind of distributed non-smooth protocols based on the relative state information of neighboring agents are proposed and analyzed. With the help of tools from Lyapunov stability theory and graph theory, it is shown that bipartite tracking consensus in the close-loop MAS can be achieved if the gain matrix of protocol is suitably constructed and the control parameters of protocol are, respectively, larger than some positive quantities depending on global information of the considered MAS. To provide some efficient criteria for consensus seeking without involving any global information, some fully distributed protocols with adaptive control parameters are further designed and discussed. Finally, numerical simulations are given for illustration.