Abstract <p>In this paper, the stabilizing laws are built for controlling the orbital orientation of a spacecraft at measuring only angular rates of roll and pitch or angular rates of yaw and pitch. The laws are obtained via analytical synthesis of control by output. The controllers by output are calculated based on a set of controllers by state using the matrix equation of coupling. The specified spectrum of a block matrix for the closed-loop control system is provided by means of similarity transformation in the form of block transposing, which made it possible to switch from control by output for a system with two inputs to control by state for a system with a single input. The conditions are given at which controllers by output exist and become stabilizing. Specific values of adjusting constants minimize the duration of transient at restrictions on angles and angular rates caused by linearization. The applicability of suggesting approach is confirmed by examples of numerical simulation. </p>