Robust Global Stabilization of the Kuramoto-Sivashinsky Equation Using Scaling Technique

Abstract

This paper addresses the problem of robust global stabilization of the Kuramoto-Sivashinsky equation subject to Neumann and Dirichlet boundary conditions. The purpose is to derive nonlinear boundary control laws which make the system globally asymptotically stable in spite of uncertainty in both the instability parameter and theanti-diffusion parameter. An approach we employ for achieving the required robustness is scaling of uncertain elements in Lyapunov- based stabilization. In this paper, we use a technique called spatially-dependent scaling in deriving robustcontrol laws. The control laws can be applied as Dirichlet like boundary control as well as Neumann like boundary control. Furthermore, it is proved that the robust boundary control laws guarantee the stability and boundedness in terms of both L2 and L∞.