In this paper, we design a model-based event-triggered controller for networked control of a linear time-invariant (LTI) system using a finite-time observer. Under the framework of hybrid dynamical systems, we show that, if the plant dynamics are detectable and stabilizable, then: 1) the zero error set is globally asymptotically stable and globally finite-time stable for the closed-loop system; 2) the closed-loop system is robust to small state perturbations; 3) the state of the plant converges to a neighborhood of the origin that can be made arbitrarily small; 4) the number of transmissions through the network is finite. We illustrate these results through numerical simulations.