In order to meet the requirement for higher thickness accuracy in cold rolling processes, it is strongly desired to have high performance in control units. To meet this requirement, we have considered an output regulating control system with a roll-eccentricity estimator for each rolling stand of tandem cold mills. Considering entry thickness variation as well as roll eccentricity as the major disturbances, a synthesis of multivariable control systems is presented based on H$sub$$infty$/ control theory, which can reflect the knowledge of input direction and spectrum of disturbance signals on the design. Then, to reject roll eccentricity effectively, a weight function having some poles on the imaginary axis is introduced. This leads to a non-standard H_ control problem, and the design procedures for solving this problem are analytically presented. The effectiveness of the proposed control method is evaluated through computer simulations and compared to that of the conventional LQ control and feedforward control methods for roll eccentricity.