Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology.Based on Lyapunov-Krasovslii functional and Lyapunov-Razumikhin functions respectively,consensus criterions in the form of linear matrix inequality (LMI) are obtained for the system with time-varying communication delays under static interconnection topology converging to the leader's states.Moreover,the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovslii functional.Numerical simulations present the correctness of the results.