Consensus of linear multi-agent systems with fully distributed control gains under a general directed graph

In this paper, we study the leaderless consensus problem for general linear multi-agent systems under a general directed graph. A distributed consensus algorithm with gain adaption is proposed. A novel integral-type Lyapunov function is constructed to study the consensus convergence. The control gains are varying and updated adaptively by distributed adaptive laws. The proposed algorithms require no global information and thus can be implemented in a fully distributed manner.