is
      observation to drive the system to its homoclinic orbit, and then let the
      dynamics of the pendulum carry us to the upright equilibrium.  Recall that
      the homoclinic orbit has energy $mgl$ -- let's call this our
      <i>desired</i> energy:$$E^d = mgl.$$  Furthermore, let's define the
      difference between our current energy and this desired energy as
      $\tilde{E} = E - E^d$, and note that we still have $$\dot{\tilde{E}} =
      \dot{E} = u\dot\theta.$$  Now consider the feedback c