Asynchronous event-triggered control (AETC) is a control strategy proposed for wireless networked implementations whose sensor nodes have limited energy supplies. Local thresholds allow the sensors to sample and to transmit local measurements independently of each other. AETC uses only one bit for each measurement transmission while still guarantees stability and predesigned performance of the closed-loop. In this paper, we extend the previous work on AETC, and study the stability and ℒ2-performance of periodic asynchronous event-triggered control (PAETC) for implementations with disturbances. In PAETC, the local event-triggered conditions are verified periodically at every sampling time. A dynamic controller is introduced to the PAETC framework, and the decision to transmit the controller outputs is also included in the asynchronous event-triggered mechanism to save network bandwidth. The developed theory is illustrated in a numerical example.