We address the robust stabilization of nonlinear systems subject to exogenous inputs using event-triggered output feedback laws. The plant dynamics is affected by external disturbances, while the output measurement and the control input are corrupted by noises. The communication between the plant and the controller is ensured by a digital channel. The feedback law is constructed in continuous-time, meaning that we ignore the communication network at this step. We then design the sampling rule to preserve stability. Two implementation scenarios are investigated. We first consider the case where the sampling of the plant measurements and of the control input are generated by the same rule, which leads to synchronous transmissions. We then study the scenario where two different laws are used to sample the measurements on the one hand, and the control
input on the other hand, thus leading to asynchronous transmissions. In both cases, the transmission conditions consist in waiting a fixed amount of time after each sampling instant and then in checking a state-dependent criterion: when the latter
is violated, a transmission occurs. In that way, Zeno phenomenon is a fortiori excluded. The proposed hybrid controllers are shown to ensure either an input-to-state stability property or an Lp stability property, depending on the assumptions. The results are applied to linear time-invariant systems as a particular case, for which the assumptions are formulated as linear matrix inequalities. The proposed strategy encompasses time-driven (and so periodic) sampling as a particular case, for which the results are new. The effectiveness of the approach is illustrated on simulations for a physical system.