Abstract: Consensus problems for mobile multi-agent systems are very practically significant in complicated kinetics systems. A consensus protocol for the first-order and the second-order discrete-time system with diverse delays in directed communication network topology is proposed. Based on the protocol, the discrete transfer function is obtained. Then generalized Nyquist criterion and Gershgorin disc method is applied to analysis the system in frequency domain. A sufficient condition is deduced for consistency convergence of the transfer function, and concrete constraint range of communication delays is given out. The simulation results show the correctness of the proposed ideas.