A note on discrete-time stabilization of Hamiltonian systems

In this paper we present some preliminary results on the stabilization problem for Hamiltonian systems using approximate discrete-time models. The issues of constructing a discrete-time model for Hamiltonian system are in general different from those for dissipative systems. We propose an algorithm for constructing an approximate discrete-time model, which guarantees the Hamiltonian conservation, and apply the algorithm to a class of port-controlled Hamiltonian systems. We illustrate the usefulness of the algorithm in designing a discrete-time controller to stabilize the angular velocity of a rigid body