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The paper is devoted to the theoretical problem of designing a robust asymptotic tracking control system for a rotational motion of a 2DOF underactuated linear mechanical system with parametric uncertainties. The mathematical formulation of the problem is motivated by the attitude control problem of an earth observation satellite with a solar panel. It is assumed that all the parameters of the plant model are uncertain and the plant single input is additively disturbed by an unknown constant torque. By employing the general regulator theory in the state space setup combined with the concept of the structured singular value, we develop a robustly stabilizing and robustly asymptotically tracking error feedback controller. The rotation of the main rigid body of the mechanical system is to asymptotically track a harmonically changing reference signal. The obtained theoretical results are successfully tested on two numerical examples and computations are performed in Matlab.