A satellite in a circular Earth orbit is under consideration. The three–axis stabilization of the satellite in orbital coordinate system with the attitude control system using moments of Lorentz forces is studied. The linearized mathematical model of this system is time-varying linear system. Unlike the earlier works on this problem, we propose the novel rigorous approach based on the fact that the considered linearized system belongs to a certain class of time-varying systems. Systems of this class can be reduced to time-invariant systems of larger order. For obtained time-invariant system, controllability is analyzed, and the optimal stabilization algorithm based on the LQR method is constructed. The results of numerical simulation demonstrate the efficiency of the proposed approach.

圆形地球轨道上的卫星正在考虑中。研究了利用洛伦兹力力矩的姿态控制系统对卫星在轨坐标系中的三轴稳定度。该系统的线性数学模型是时变线性系统。与早期关于此问题的工作不同，我们基于所考虑的线性化系统属于一类时变系统这一事实，提出了一种新颖的严格方法。此类系统可以简化为较大阶的时不变系统。针对获得的时不变系统，分析了系统的可控性，构造了基于LQR方法的最优稳定算法。数值仿真结果证明了该方法的有效性。