In this paper, we consider the consensus of leader-following multi-agent systems. We extend a window-based periodic event-triggered strategy to leader-following multi-agent systems. This strategy was originally proposed by Seidel et al. for leaderless consensus. We give an upper bound on the evolution of the Lyapunov function and present the consensus condition for our considered leader-following system. This is accomplished by adding the previous information to the general triggering conditions and allowing an increase in the Lyapunov function within a local range as long as a decreasing tendency is still guaranteed. Finally, some simulation examples are given to demonstrate that the proposed approach ensures system consensus while reducing the communication costs.
Wang et al. (Sat,) studied this question.