Stabilization of invariant tori in Hamiltonian systems under persistently acting disturbances

The problem of invariant tori stabilization in multi-degrees-of-freedom Hamiltonian systems under uniformly bounded disturbances is considered. The main result gives the conditions for ultimate boundedness of trajectories of controlled system under disturbances with respect to the torus to be stabilized. The estimates for region of attraction and ultimate bound are obtained. The essential role in the proof is played by Lemma 1, which gives the conditions for ultimate boundedness with respect to a given nonnegative smooth function V without assumption of negative (semi)-definiteness of time derivative of V. Copyright (C) 2001 John Wiley & Sons, Ltd.