Towards a digital and flexible implementation of triggering conditions for multi-agent systems, we propose a sampled-data framework with discrete-time controllers and event detectors. An asynchronous sampling mechanism between agents is considered, where the sampling period and triggering parameters are allowed to be chosen by each agent independently. It is shown that consensus can be reached under the proposed control and communication schemes for graphs that contain a directed spanning tree. Simulation results are given to illustrate the utility of the proposed method. (C) 2017 Elsevier Ltd. All rights reserved.