This paper studies the stability analysis of the decentralized event-triggered H control with communication delays using the quadratic convex approach. Unlike the decentralized event-triggered mechanism (ETM), which only uses the information from the sensor itself by considering the communication topology of the wireless sensor network, a more general decentralized ETM is first proposed by using the information from both the sensor itself and its neighbours. Then, a time-delay system model with parameters of the decentralized ETM, directed graph information, communication delays and external disturbances is presented. In addition, novel delay-dependent asymptotic stability criteria are derived by using the augmented Lyapunov–Krasovski functional (LKF), which contains the cross terms of variables and quadratic terms multiplied by a higher degree scalar function. Unlike some prior results using the first-order convex combination property, our derivation applies the quadratic convex approach with the augmented LKF, which results in less conservatism. Moreover, sufficient conditions for the co-design of the controller and the decentralized ETM are obtained. Finally, numerical examples confirm the effectiveness of the proposed method.