This paper proposes an event-triggered control for multi-agent systems in which all agents have an identical linear dynamic mode. The asynchronous event-triggered control algorithms are proposed based on the triggering time sequences of all agents. The main contribution of this paper is to extend the event-triggered control method to investigate general linear multi-agent systems. First, by applying variable substitution method, we give the asynchronous triggering conditions. Based on the conditions, the consensus can be achieved both under fixed and switching topologies. Meanwhile, all the proposed event-triggered algorithms can exclude Zeno behaviours of the closed-loop systems. Then, the asynchronous results are applied to cope with formation control problem. Finally, numerical simulations are presented to illustrate the effectiveness of the part event-triggered protocol designs.