Consensus tracking of multi-agent systems with time delays and disturbances

This paper investigates leader-following multi-agent systems consensus problems with time delays and disturbances. It is assumed that the directed communication topologies are connected. Based on algebraic graph theory, matrix theory, Razumikhin theorem and Lyapunov function method, it is proved rigorously that the systems would reach consensus with the protocol we designed if some conditions are satisfied. Finally, a numerical simulation is given to prove the effectiveness of the obtained theoretical results.