Modern marine dynamic positioning (DP) systems are commonly constructed on the basis of nonlinear asymptotic observers. The primary reason for the observer's employment is to restore deficient information concerning the unmeasured velocities of the vessel. Nevertheless, using a number of separate items in addition to the observers, it is also possible to achieve desirable dynamical features of the closed-loop connection. The paper is devoted to the problem of synthesis of these items for marine vessels, which are controlled by DP systems under the action of sea wave disturbances. The essence of the problem is to identify a transfer matrix of the adjustable corrective item (filter), minimising the intensity of the control action determined by high-frequency sea wave components. The correspondent dynamic of a closed-loop system realises an economical regime of vessel motion with the aim to reduce general fuel consumption and to prevent the wearing down of actuators. A specialised approach for designing the filters is proposed that provides asymptotic stability and the integral action of a control. Applicability and effectiveness of this approach are illustrated by the practical example of DP system synthesis.