Multi-agent systems cooperation to achieve global goals is usually limited by sensing, actuation, and communication issues. At the local level, continuous measurement and actuation is only approximated by the use of digital mechanisms that measure and process information in order to compute and update new control input values at discrete time instants. Interaction with other agents or subsystems takes place, in general, through a digital communication channel with limited bandwidth where transmission of continuous-time signals is not possible. Additionally, communication channels may be subject to other imperfections such as time-varying delays. This paper considers the problem of consensus (or synchronization of state trajectories) of multi-agent systems that are described by general linear dynamics and are connected using undirected graphs. An event-triggered consensus protocol is proposed, where each agent implements discretized and decoupled models of the states of its neighbors. This approach not only avoids the need for continuous communication between agents but also provides a decentralized method for transmission of information in the presence of time-varying communication delays where each agent decides its own broadcasting time instants based only on local information. This method gives more flexibility for scheduling information broadcasting compared to periodic and sampled-data implementations. The use of discretized models by each agent allows for a periodic event-triggered strategy where continuous actuation and continuous measurement of the states are not necessary.