Distributed sampled-data control of Kuramoto-Sivashinsky equation under the point measurements

We consider sampled-data distributed control of nonlinear PDE system governed by Kuramoto-Sivashinsky equation under point measurements and distributed in space shape functions. It is assumed that the sampling intervals in time and in space are bounded. We derive sufficient conditions ensuring local exponential stability of the closed-loop system in terms of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii method. Moreover, we give a bound on the domain of attraction. As it happened in the case of heat equation, the time-delay approach to sampled-data control and the descriptor method appeared to be efficient tools for the stability analysis of the sampled-data Kuramoto-Sivashinsky equation.