Exponential stability for linearized Korteweg-de Vries-ODE system

In this paper, a class of linearized Korteweg-de Vries equation is designed to be a dynamic boundary feedback controller to stabilize a pendulum, which is described as a second order ODE. The semigroup approach is adopted to show that the linear operator constructed in analyzing well-posedness and stability of the target system.For both the state and output feedback boundary controllers, exponential stability analysis in the sense of the corresponding norms for the resulting closed-loop system are provided.