Asynchronous event-triggered control (AETC) is a triggering strategy for the feedback channel of a closed-loop control system. AETC aims at reducing transmissions compared with time-triggered control strategies and listening time compared with other event-triggered control strategies. This work is an extension of the asynchronous event-triggered control [6] on reducing periodic listening time spent for the threshold update signal. In this work, by introducing an autonomous time-varying threshold update mechanism at every node, the listening time can totally be removed while still guaranteing a pre-designed control performance. A numerical example is shown to illustrate the developed strategy.