  The moment method is used to prove the exact controllability of a wide class
of bidimensional linear dispersive PDE's posed on the two-dimensional torus
$\mathbb{T}^{2}.$ The control function is considered to be acting on a small
vertical and horizontal strip of the torus. Our results apply to several
well-known models including some bidimesional extensions of the Benajamin-Ono
and Korteweg-de Vries equations. As a by product, the exponential
stabilizability with any given decay rate is also established in
$H^{s}_{p}(\mathbb{T}^{2}),$ with $s\geq 0,$ by constructing an appropriated
feedback control law.
