We describe the effect of physical dissipation on stability of
equilibria which have been stabilized, in the absence of damping,
using the method of controlled Lagrangians. This method
applies to a class of underactuated mechanical systems including
“balance” systems such as the pendulum on a cart. Since
the method involves modifying a system’s kinetic energy metric
through feedback, the effect of dissipation is obscured.
In particular, it is not generally true that damping makes a
feedback-stabilized equilibrium asymptotically stable. Damping
in the unactuated directions does tend to enhance stability,
however damping in the controlled directions must be “reversed”
through feedback. In this paper, we suggest a choice
of feedback dissipation to locally exponentially stabilize a class
of controlled Lagrangian systems
