Sampled-data control of 2D Kuramoto-Sivashinsky equation under the averaged measurements

This paper deals with sampled-data control of 2D Kuramoto-Sivashinsky equation over a rectangular domain Omega. We suggest to divide the 2D rectangular Omega into N sub-domains, where sensors provide spatially averaged state measurements to be transmitted through communication network. 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, 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.