In this paper, a new output-based adaptive event-triggered control (AETC) method is introduced for a general class of nonlinear systems. A crucial aspect of the AETC method is to design an event-triggering mechanism (ETM) determining when the sampling operation should be done. The proposed ETM, which is derived from the finite-gain L₂ stability condition, reduces the number of updating operations while the performance of the closed-loop system is maintained. Thanks to the Lipschitz property, the avoidance of Zeno behavior is also guaranteed by introducing a positive lower bound on the inter-event times. This lower bound is obtained by solving a set of proposed ordinary differential equations. In addition, the proposed method is developed into robust control of uncertain linear time invariant (LTI) systems through some matrix inequalities (such as linear matrix inequalities (LMIs)). Finally, several numerical simulations are presented to demonstrate the ability of the proposed method to achieve greater average inter-event times and to preserve the system performance rather than other references.