The paper presents a solution to the problem of synthesis of control with respect to the sliding interval length for the optimization of a class of discrete linear multidimensional objects with a quadratic performance criterion. The equation of motion of a closed multidimensional discrete system in the general non-stationary case is derived based on the length of the optimization interval and their main properties. The closed-loop is fitted with a signal representing the predicted values averaged over the whole sliding interval of optimization with a certain weight. A problem with a sliding optimization interval may not require a real-time solution by means of a sequence of solutions on compressed intervals. Therefore, the study of control systems with optimization on a sliding interval is of undoubted interest for a number of practically important control problems.