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

✍ Scribed by Panagiotis D. Christofides; Antonios Armaou

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 211 KB
• Volume: 39
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(99)00108-5

✦ Synopsis

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 su cient stability condition is satisÿed, 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 ÿnite-dimensional approximations of the KSE which are obtained through Galerkin's method. The theoretical results are conÿrmed by computer simulations of the closed-loop system.