Traditionally, the problem of the satellite control, its reorientation from one angular position into another, is solved, as a rule, with the use of Pontryagin maximum principle. An example of its application is the algorithm for the control reorientation of the Resurs-P satellite equipped with the inertial effectors (control momentum gyros). On the whole, the algorithm implements the programmed rotations around the Euler axis. The whole interval of the given turn consists of three phases, including "speedup", motion at a constant angular velocity and "slowdown". "Speedup" and "slowdown"phases, in their turn, are also divided into three sub-phases. At the first of them the motion goes on with acceleration, increasing linearly in the absolute terms, at the second sub-phase the acceleration is constant, and at the third one, it decreases (in absolute terms) down to zero. Solution to a two-point boundary problem is a precondition for building of the optimal program for control of a satellite 's angular motion in its reorientation. In order to eliminate the necessity for solving of the two-point boundary problem and to build a closed system for the satellite motion control in its reorientation in a feedback form, the present article poses and solves the task of synthesis of a discrete system, which is linear (both in state and control) and based on the power-efficient algorithm for control by the noisy measurements, developed by the author. According to the algorithm, the spur minimum of the covariance control matrix at each step was chosen as the system's quality index. The author introduced an auxiliary dynamic system and set its parameters. The optimal closed-loop control law was chosen in a linear form - control at the current step was defined as an algebraic sum of the control at the previous step and the weighted difference of the state vectors of the specified and auxiliary systems at the current step. The measurable state vector of the set system was fully observable and comprised random measurement errors, such as a centered discrete white noise. The reorientation time was not explicitly defined. There were no limitations for the control parameters. The power-efficient control algorithm proved to be quite constructive, since the specified quality index of the system was, at the same time, a positive definite Lyapunov function, which added a condition of the asymptotic stability to the whole system. The author developed a discrete model of the undisturbed angular motion of the Resurs-P spacecraft equipped with three pairs of the control momentum gyros and mathematically modeled the power-efficient control algorithm for the spacecraft reorientation. The results of modeling confirmed the efficiency of the proposed algorithm. For simplicity reasons, the angular position of the satellite is defined by the angles of rotation around the body axes, and not by the quaternions.