  This paper addresses sampled-data control of 2D Kuramoto-Sivashinsky equation
over a rectangular domain. We suggest to divide the 2D rectangular into N
sub-domains, where sensors provide spatially averaged or point state
measurements to be transmitted through communication network to the controller.
Note that differently from 2D heat equation, here we manage with sampled-data
control under point measurements. We design a regionally stabilizing controller
applied through distributed in space characteristic functions. Sufficient
conditions ensuring regional stability of the closed-loop system are
established in terms of linear matrix inequalities (LMIs). By solving these
LMIs, we find an estimate on the set of initial conditions starting from which
the state trajectories of the system are exponentially converging to zero. A
numerical example demonstrates the efficiency of the results.
