Feedback control of the Kuramoto-Sivashinsky equation

This work focuses on linear finite-dimensional output feedback control of the Kuramoto-Sivashinsky equation (KSE) with periodic boundary conditions. Under the assumption that the linearization of the KSE around the zero solution is controllable and observable, linear finite-dimensional output feedback controllers are synthesized that achieve stabilization of the zero solution, for any value of the instability parameter. The controllers are synthesized on the basis of finite-dimensional approximations of the KSE which are obtained through Galerkin's method. The performance of the controllers is successfully tested through computer simulations.