In this paper, a new method for designing robust fixed-order $\mathcal{H}_{\infty}$ discrete-time controllers is presented. The controller structure is a two-degree of freedom polynomial controller of the $RST$ type. A data-driven approach is implemented for the design process in order to capture the unmodeled dynamics that may exist with parametric models. The H infinity robust performance condition can be represented by a set of convex constraints with respect to the parameters of the RST controllers. A convex optimization algorithm can then be implemented to obtain these parameters. The proposed method is applied to a multi-axis torsional system where the goal is to control the position of the disks with variable inertia.