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

Exact controllability and stabilization for linear dispersive PDE's on the two-dimensional torus