  In this paper we introduce a new method to design control laws for non-linear
underactuated systems. Our method produces an infinite dimensional family of
control laws, whereas most control techniques only produce a finite dimensional
family. These control laws each come with a natural Lyapunov function. The
inverted pendulum cart is used as an example. In addition, we construct an
abstract system which is open loop unstable and cannot be stabilized using any
linear control law, and demonstrate that our method produces a stabilizing
control law.
