Bounded adaptive stabilization

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. As example we consider the rotational system with nonlinear dissipative force and disturbances which periodically depends on the angle. We consider also the problem of evaluating unknown external periodic torque of this rotational system. The second example is adaptive stabilization of the uniform transition of the pendulum on a cart.