On the attitude stabilization of a rigid body under control with distributed delay

The problem of attitude stabilization of a rigid body is under consideration. The issue of realizing such a control system of the PID-controller type with distributed delay (integral term) is addressed. A theorem on the asymptotic stability of the stabilized position of the body, which justifies the possibility of constructing the desired control system, has been proven. The effectiveness of the constructed control with a distributed delay is confirmed by numerical modeling.