This paper is concerned with identifying linear time-invariant systems working in a networked environment. It turns out that the running mode of actuators in the networked environment is a decisive factor in forming such networked identification problems with very different complexities. Given this, the focus of the paper is placed upon the configuration of event-driven actuators subject to random network-induced delays and packet dropouts. Then the associated networked identification problem is to identify continuous-time linear time-invariant models from the general non-uniformly non-synchronized sampled data. A modified version of the simplified refined instrumental variable method is developed to solve this networked identification problem, with its performance being verified via simulation results.