This paper focuses on the distributed fault-tolerant leader-following synchronisation problem for linear multi-agent systems (MASs) with the event triggering strategy. Firstly, in order to compensate effectively for the actuator faults and bounded inputs from the leader, a distributed event-triggered algorithm with adaptive techniques is proposed. Secondly, the trigger function with adaptive parameters is designed to enhance the self-regulation of the trigger mechanism, which is relevant to the state of the agents and time, but not to the number of agents. Then, it is demonstrated that the developed consensus protocol can achieve not only the synchronisation of agents without continuous communication, but also the exclusion of Zeno behavior. Finally, example of numerical simulation illustrates the effectiveness of the presented control protocol. [ABSTRACT FROM AUTHOR]