A theoretical and an empirical application of the speed control of a single-shaft turbo-jet engine was done using an observer for Linear Quadratic Gausian(LQG) that is one of the robust control fields. Based on a general controller design with state feedback, a controller with output feedback was designed to find out a sufficient condition in finding an Asymptotic Stability After defining of the total system through the modeling of a real turbo-jet engine, a Tracking Control was carried out. Furthermore, a saturation of the control input was theoretically considered in the output feedback controller to simulate more similar real condition.