This paper presents an application of LMI-based techniques to the mixed $H_2/ H_infty$ control of an inverted pendulum. The linear model of the inverted pendulum represented by an LFR(Linear Fractional Representation) model of uncertainties is derived. Considered uncertainties are three nonlinear components and a parameter uncertainty Augmenting the LFR model by adding weighting functions, we get a generalized plant, for which we design a mixed $H_2/ H_infty$ controller using the LMI technique. To evaluate control performances and robust stability of the mixed $H_2/ H_infty$ controller designed, we compare it with the $ H_infty$controller through the simulation and experiment. The mixed $H_2/ H_infty$ controller shows the better control performances and robust stability than the $H_infty$controller in the sense of pendulum angle.