Stabilization of the coupled ODE-linearized KdV system

Abstract

Abstract This paper considers the exponential stabilization of coupled ordinary differential equation (ODE)-linearized Korteweg-de Vries (KdV) equation system coupled at right boundary point with left boundary control. Firstly, we transfer the original system into an exponentially stable target system by backstepping transformation. Secondly, we show the existence of the kernels in forward and backward transformation. Finally, we prove the exponential stability of the closed-loop system.