Leader-following group consensus of Multi-agent systems with different time delays

In this paper, the leader-following group consensus problem is considered for multi-agent systems with different time-delays of position and velocity vectors. A new control protocol is designed to solve the group consensus for multi-agent systems. By using matrix theory and Lyapunov stability theory under the relationship between the time delays parameters and the characteristic equation, the bounds of different time delays are proposed, it is proved that the leader-following group consensus of the multi-agents systems can be achieved by the protocol in the proposed delay intervals. The main contribution of this paper is to seek the different time-delays bounds of position and velocity vectors under some assumptions for multi-agent systems.Finally, some simulation results are worked out to demonstrate our theoretical results.