Stabilization of linearized Korteweg-de Vries systems with anti-diffusion by boundary feedback with non-collocated observation

This paper addresses the problem of stabilizing a class of one-dimensional linearized Korteweg-de Vries systems with possible anti-diffusion (LKdVA for short), through control at one end and non-collocated observation at the other end. An exponentially convergent observer is designed, and then a dynamical stabilizing output feedback boundary controller is constructed based on the observer. The resulting closed-loop systems can achieve arbitrary exponential decay rate. In order to derive invertibility of the kernel function in the backstepping transformation between the observer error systems and its corresponding target systems, stabilizing of a critical case of LKdVA is considered in the Appendix, which can also be treated as a preliminary problem for the main part of this paper.