Energy control of one-degree-of-freedom oscillators in presence of bounded force disturbances

Energy level stabilization problem for one-degree-of-freedom Hamiltonian systems in presence of bounded input (force) disturbances is considered. It is shown that for arbitrary uniformly bounded force disturbances with sufficiently small bound speed-gradient control law ensures ultimate boundedness of energy error. As an auxiliary result the new sufficient conditions for ultimate boundedness of Lyapunov function along the trajectories of nonlinear nonstationary dynamical system are obtained.