Disturbance observer-based control for 2D nonlinear Kuramoto-Sivashinsky equation with average measurements

In this article, we propose a disturbance rejection approach to stabilize 2D nonlinear Kuramoto-Sivashinsky (K-S) equation over a rectangular domain. The control input suffering from the disturbance is actuated through distributed in space characteristic functions. The disturbance is estimated and based on which the disturbance is compensated. Sufficient conditions are explored to ensure the stability of the closed-loop system in terms of the linear matrix inequality (LMI).