The problem of triaxial attitude stabilization of a satellite in the orbital frame is considered. The problem is raised about the possibility of implementing such a system of electrodynamic attitude control by the type of a PID controller in which the restoring component of the control torque contains a distributed delay. A constructive analytical approach to the nonlinear stability analysis in the problem of triaxial attitude stabilization of a satellite is presented. A theorem on the asymptotic stability of the stabilized angular position of the satellite is proved. The theorem substantiates the possibility of constructing the indicated control system. Nonlinear analysis is based on the Lyapunov direct method and an original construction of Lyapunov–Krasovskii functional. The effectiveness of the designed attitude control with a distributed delay is confirmed by a computer modeling.

考虑了轨道框架内卫星的三轴姿态稳定问题。问题在于通过控制转矩的恢复分量包含分布延迟的PID控制器类型来实现这种电动姿态控制系统的可能性。提出了卫星三轴姿态稳定问题中非线性稳定性分析的建设性分析方法。一个渐近稳定性定理证明了卫星的稳定角位置。该定理证实了构建指定控制系统的可能性。非线性分析基于 Lyapunov 直接法和 Lyapunov-Krasovskii 泛函的原始构造。通过计算机建模证实了设计的具有分布式延迟的姿态控制的有效性。