The asymptotic behavior was determined in terms of the topological structure of the system, the step length and the rotation angle of the corresponding rotation matrix. Some necessary and sufficient conditions for the multi-agent systems to reach second-order consensus were found. It was shown that the asymptotic consensus appears when 0 is a simple eigenvalue of the Laplacian matrix, the step length and the rotation angle is less than the critical value which was determined by an algebraic equation. Some numerical simulations were presented to demonstrate the theoretical results. Some cases on the influence of characteristic parameters on second-order consensus were designed, which showed that the conclusion of characteristic parameters can provide important criterion and theoretical support for the control theory.