This paper studies the \({\cal{L}}_{2}-{\cal{L}}_{\infty}\) consensus problem of leader-follower multi-agent systems based on an adaptive event-triggered strategy. Firstly, the consensus problem of the multi-agent systems is transformed into the stability problem of the error system through model transformation. Secondly, an adaptive triggering mechanism is propoeed to significantly reduce redundant data transmissions through real-time tracking error-based adjustment of communication intervals. Subsequently, leveraging Lyapunov theory and matrix inequalitiesan, an \({\cal{L}}_{2}-{\cal{L}}_{\infty}\) controller is designed to achieve disturbance rejection and peak constraint performance. Finally, the relationship between the optimal \({\cal{L}}_{2}-{\cal{L}}_{\infty}\) performance index and the maximum sampling period is discussed, and the effectiveness of the proposed method is verified by numerical examples.
