ASYMPTOTIC STABILIZATION OF THE DESIRED UNIFORM MOTION IN UNDERACTUATED HAMILTONIAN SYSTEMS BY LINEAR FEEDBACK

In some cases the desired uniform motion may be described by a pair of first integrals of the system with zero control input. These two integrals and the integration of nonlinear function of saturation are 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 and linear in a small viciniti of the desired motion. This method is applied to stabilize rotating body beam, for damping the oscillations of blades of an elastic propeller and for stabilization of the uniform transition of the pendulum on a cart.