In this paper, robust depth and course controllers of AUV(autonomous underwater vehicles) using LMI-based H$_{infty}$ servo control are proposed. The $H_{infty}$ servo problem is modified to an $H_{infty}$ control problem for the generalized plant that includes a reference input mode, and then a sub-optimal solution that satisfies a given performance criteria is calculated by LMI(Linear Matrix Inequality) approach. The robust depth and course controllers are designed to be satisfied the robust stability about the modeling error generated from the perturbation of the hydrodynamic coefficients and the robust tracking property under sea wave and tide disturbances. The performances of the designed controllers are evaluated by computer simulations, and these simulation results show the applicability of the proposed robust depth and course controller.