In this paper,the consensus for multi-agent systems under second-order dynamics with delays are investigated.We investigate the consensus of the protocol with relative damping.Sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to give the upper bound for time-varying communication delays which guarantees all the agents asymptotically reach consensus under fixed undirected topology and switching undirected topology,respectively.Finally,simulation is provided to illustrate the effectiveness of our theoretical results.