In this paper, sufficient conditions for the existence of stabilizing controls for one class of nonstationary difference systems with homogeneous and linear functions in the right-hand sides are derived using decomposition and the averaging method. It is assumed that only part of the state variables can be measured for the implementation of control. To prove asymptotic stability, the Lyapunov function for the original system is constructed using the corresponding functions for isolated subsystems. Moreover, the Lyapunov function for the nonstationary homogeneous difference subsystem is constructed on the basis of the corresponding function for the averaged system of ordinary differential equations.