The mixed $H_2/ H_infty$ control method is one of positive approaches to design a controller having both the$H_2$-performance and the $H_infty$-robust stability. In this paper, Firstly, The tracking Performance to be designed has been represented as $H_2$-norms for the plants with uncertainties. Secondly, $H_infty$-norm have been set up in order to ensure the robust stabilities. The mixed digital controllers have been designed for an inverted system. The mixed $H_2/ H_infty$digital controller for the inverted pendulum system was intended to stabilize the unstability of the plant together with the good tracking Performance.