Consensus of Second-Order Delayed Multi-Agent Systems with Leader-Following

In this paper, a second-order consensus algorithm of multi-agent dynamical systems with leader-following is presented. With the hypothesis of a directed weighted connected graph composed of n agents together with a leader and the leader as a globally reachable node, the consensus algorithm with heterogeneous input delays is studied in the frequency domain. By applying Gershgorin disc theorem and curvature theory, decentralized consensus conditions for the multi-agent systems with asymmetric coupling weights are obtained. Finally, a simulation example is used to show the design of the parameters and the validity of the result.