Taking the firstorder inverted pendulum as the controlled object, the state equation modeling process of the inverted pendulum was introduced in detail. On this basis, the output feedback controller theory based on state observer was introduced. The process of establishing state observer was analyzed, and the separation theorem was explained in detail when the system could be controlled and viewed. Finally, based on the separation theorem, the dynamic characteristic equation of the closedloop system of the output feedback controller based on the firstorder inverted pendulum was established. Taking the obtained dynamic characteristic equation as the research object, the simulation study of the system was carried out by using MATLAB. The results show that the closedloop system with the state estimation value instead of the real state of the system still has the progressive stability and good dynamic performance of the originally closedloop system.