This paper puts forward a new free‐weight matrix method used to analyse Network control systems (NCSs) with the H∞ performance index level based on event‐driven control. Firstly, design a relative triggering mechanism contain the measured output for a linear system with external disturbances. Secondly, in order to reduce the conservativeness an appropriate Lyapunov‐Krasovskii function is constructed. For the integral term generated after the above functional derivation, the free‐weight matrix inequality is selected for scaling. Finally,the sufficient condition that the closed‐loop system represented by the linear matrix inequality (LMI) satisfies the H∞ performance index and the solution of the controller are obtained.The validity of the scheme is confirmed by a given numerical case.