We formulate the discrete-time output feedback controller design problem where the desired accuracy of controlled variables in the mean-square sense is guaranteed in the presence of bounded polyharmonic disturbances with a priori unknown number of harmonics, amplitudes, and frequencies. The amplitudes of the harmonics must satisfy a condition that results in the boundedness of the power of each polyharmonic component. The solution is based on the discrete-time H∞-optimization procedure by properly choosing the corresponding weighting matrices of the minimax cost criterion. Numerical solution in state-space is based on the method of linear matrix inequalities, using the LMI Control Toolbox (MATLAB application). We give a synthesis algorithm for a digital controller in the LMI Control Toolbox package and a numerical example for the main drives pipe-rolling mill.