Asymptotic stabilization of the desired uniform rotation by linear and nonlinear feedback

In some cases the desired uniform motion may be described by a pair of first integrals of the system with zero control input. The linear-quadratic combination of these two integrals is used to construct Lyapunov function. The control is designed from the condition of decreasing Lyapunov function on the trajectories of the closed loop system. This control may be chosen a priori bounded. This method is applied to stabilize circular motion of a satellite around gravitational center, for stabilization inertia wheel pendulum and for swinging a pendubot.