The paper adresses the problem of stabilization of a specific target positi
on of underactuated Lagrangian or Hamiltonian systems, We propose to solve
the problem in two steps: first to stabilize a set with the target position
being a limit point for all trajectories originating in this set and then
to switch to a locally stabilizing controller. We illustrate this approach
by the well-known example of inverted pendulum on a cart. Particularly, we
design a controller which makes the upright position of the pendulum and ze
ro displacement of the cart a limit point for almost all trajectories. We d
erive a family of static feedbacks such that any solution of the closed loo
p system except for those originating on some two-dimensional manifold appr
oaches an arbitrarily small neighbourhood of the target position. The propo
sed technique is based on the passivity properties of the inverted pendulum
. A possible extension to a more general class of underactuated mechanical
systems is discussed. Copyright (C) 2000 John Wiley & Sons, Ltd.