Abstract: An impulsive control algorithm is proposed for second-order multi-agent systems with communication and input time-delays. The consensus criteria for getting such algorithm are analyzed. In the meantime, the effects of communication and input time-delays on the consensus performance of second-order multi-agent systems are discussed. It is shown that communication time delay will be more important than input time-delay in connection with determining consensus dynamics of second-order multi-agent systems. Explicitly, when there is no communication time-delay, second-order multi-agent systems will be able to achieve dynamic consensus with a nonzero constant velocity of individual agent. Nevertheless, so long as there exists communication delay, the velocity consensus state of the system will be zero under certain condition. In addition, an even more interesting fact will be found that either the communication or input time-delay will enhance the synchronization performance of the second-order multi-agent systems under undirected network topology. Finally, some numerical simulations are used to verity the effectiveness of the theoretical result.

Key words: second-order multi-agent system, impulsive consensus algorithm, input-communication time-delay, time-delay effect