Global stabilization of the Kuramoto-Sivashinsky equation via distributed output feedback control

This work addresses the problem of global exponential stabilization of the Kuramoto-Sivashinsky equation (KSE) subject to periodic boundary conditions via distributed static output feedback control. Under the assumption that the number of measurements is equal to the total number of unstable and critically stable eigenvalues of the KSE and a necessary and sufficient stability condition is satisfied, linear static output feedback controllers are designed that globally exponentially stabilize the zero solution of the KSE. The controllers are designed on the basis of finite-dimensional approximations of the KSE which are obtained through Galerkin's method. The theoretical results are confirmed by computer simulations of the closed-loop system.