Nonlinear Control with Distributed Delay for the Angular Stabilization of a Rigid Body

The problem of the angular stabilization of a rigid body with an arbitrary triaxial ellipsoid of inertia is solved. The control strategy is based on a kind of a proportional integral derivative (PID) controller, where the conventional integral element is replaced with a more flexible control option, which assumes the presence of a distributed delay (integral term) in the control torque. In addition, a nonlinear uniform restoring torque is used for the first time instead of the usual linear restoring torque. Analytical substantiation of the asymptotic stability of the program motion involves a special construction of the Lyapunov–Krasovskii functional. A theorem is proved that provides sufficient conditions for the asymptotic stability of the program mode of angular motion of the body in the form of constructive inequalities with respect to the control parameters. The effectiveness of the constructed control is demonstrated, which provides both the high speed and smoothness of transient processes.