In this paper, the event-triggered consensus problem is studied for multi-agent systems with general linear dynamics under a general directed graph. Based on state feedback, we propose a decentralized event-triggered consensus controller (ETCC) for each agent to achieve consensus, without requiring continuous communication among agents. Each agent only needs to monitor its own state continuously to detefmine when to trigger an event and broadcast its states to its out-neighbors. The agent updates its controller when it broadcasts its states to its out-neighbors or receives new information from its in neighbors. The ETCC can be implemented in multiple steps. it is proved that under the proposed ETCC there is no Zeno behavior exhibited. To relax the requirement of continuous monitoring of each agent's own states, we further propose a self-triggered consensus controller (STCC). Simulation results are given to illustrate the theoretical analysis and show the advantages of the event-triggered and self-triggered controllers proposed in this paper. (C) 2016 Elsevier Ltd. All rights reserved.