For second-order multi-agent systems, a fast consensus protocol using both current states and outdated states
is proposed. The fast consensus protocol is analyzed under a directed communication graph. Based on the frequentlydomain
analysis and matrix theory, the necessary and sufficient, condition for second-order multi-agent systems converging
to stationary consensus and dynamical consensus are obtained respectively. Moreover, it is shown that the system converges
to stationary consensus and dynamical consensus faster than the standard consensus protocol if the outdated states are chosen
properly. Simulation results show the effectiveness of the protocol.