Controlling nonlinear water waves: boundary stabilization of the Korteweg-de Vries-Burgers equation

Abstract

The problem of global exponential stabilization by boundary feedback for the Korteweg-de Vries-Burgers equation on the domain [0,1] is considered. We derive a control law of the form u(0)=u/sub x/(1)=u/sub xx/(1)-k[u(1)/sup 3/+ u(1)]=0, where k is a sufficiently large positive constant, and prove that it guarantees L/sup 2/-global exponential stability, H/sup 1/-global asymptotic stability, and H/sup 1/ semi-global exponential stability. The closed-loop system is shown to be well posed.