Leader-follower consensus control of multi-agent systems with extended Laplacian matrix

This paper studies the leader-follower consensus problem of identical linear time invariant multi-agent systems. A directed graph is used to model the communication topology and a kind of extended graph Laplacian matrix is introduced. By performing a variable transformation, the consensus problem is converted to a stabilization problem. Sufficient conditions are proposed based on the Lyapunov stability analyses and algebraic graph theory. The effectiveness of the theoretical results is illustrated via numerical simulations.