This paper investigates the event-based control for network systems. Edge-based approach is utilized to predict the value of edge state between two event instants. Different from the node-based approach, it can significantly reduce the communication burden at event instants. Based on the small gain theorem, the closed-loop system is expressed as the feedback interconnection of a linear time-invariant system and an operator. The operator describes the unstable component and has an upper bound in L 2 space and the control gain is designed, such that the feedback interconnection is stable. Furthermore, we adopt the integral quadratic constraints to describe the correlation between output and input of the operator. And the Kalman-Yakubovich-Popov Lemma is adopted to transform the infinite dimensional stability condition into one inequality. The designed event-triggering condition and distributed control law can ensure that a network system achieves synchronization. The effectiveness of the communication protocol and control strategy is illustrated by a numerical example.