Robust stabilization the Korteweg–de Vries–Burgers equation by boundary control

Abstract

The problem of robust global stabilization by nonlinear boundary feedback control for the Korteweg–de Vries–Burgers equation on the domain [0,1] is considered. The main purpose of this paper is to derive nonlinear robust boundary control laws which make the system robustly globally asymptotically stable in spite of uncertainty in the system parameters. Furthermore, we show that the proposed boundary controllers guarantee L 2-robust exponential stability, L ∞-robust asymptotic stability and boundedness in terms of both L 2 and L ∞.