  We study the linear Zakharov--Kuznetsov equation with periodic boundary
conditions. Employing some tools from the nonharmonic Fourier series we obtain
several internal observability theorems. Then we prove various exact
controllability and rapid uniform stabilization results by applying a duality
principle and a general feedback construction. The method presented here
introduces a new insight into the control of dispersive equations on
two-dimensional cases and may be adapted to more general equations.
