As for general linear second-order multi-agent systems,a distributed impulse consensus control algorithm with sampled displacement information is designed.By using the methods of spectral analysis and quasi-periodic homogeneous Lyapunov function,the criteria for achieving second-order consensus are given, which reveal the mechanism of quantitative effects of the sampling period,the controller gain and the eigenvalue of Laplace matrix on achieving second-order consensus.The influence of the sampling period and uncertainties of system parameters on the distributed impulse consensus algorithm is further analyzed,and the sufficient conditions for achieving robust second-order consensus are given in the form of low-dimensional linear matrix inequalities.Finally,numerical examples have verified the proposed theoretical results.