  Fringing field has to be taken into account in the formulation of
electrostatic parallel-plate actuators when the gap separating the electrodes
is comparable to the geometrical dimensions of the moving plate. Even in this
case, the existing formulations often result in complicated mathematical models
from which it is difficult to determine the deflection of the moving plate for
given voltages and therefore to predict the necessary applied voltages for
actuation control. This work presents a new method for the modeling of fringing
field, in which the effect of fringing field is modeled as a serial capacitor.
Numerical simulation demonstrates the suitability of this formulation. Based on
this model, a robust control scheme is constructed using the theory of
input-to-state stabilization (ISS) and back-stepping state feedback design. The
stability and the performance of the system using this control scheme are
demonstrated through both stability analysis and numerical simulation.
