The tracking control of second-order multi-agent systems with time-delays

This paper is devoted to the consensus problem of the second-order multi-agent with leader and time-delays. By applying the frequency-domain method, some sufficient conditions for consensus of systems are given. And the upper bound of time-delays is deduced, which depends on the largest eigenvalue of the sum matrix of Laplacian matrix and the adjacency matrix between leader and followers. Finally, the effectiveness of conclusion is verified through the numerical simulation experiments.