The consensus problem with general linear dynamics and undirected graphs is studied in this paper by means of event-triggered control strategies. A novel consensus protocol is proposed, where each agent implements a model of the decoupled dynamics of its neighbors. Under this control strategy, transmission of information does not occur continuously but only at discrete points in time. The approach presented in this paper provides both a decentralized control law and a decentralized communication policy. We are able to design thresholds that only depend on local information and guarantee asymptotic consensus. Positive inter-event times are guaranteed for particular cases of the linear dynamics. In an extension, a positive constant is added to the thresholds in order to exclude Zeno behavior for general linear dynamics. The difference between agents trajectories can be bounded in this case and bounds on the state disagreement are derived. Published by Elsevier Ltd.