Boundary control for a kind of coupled PDE-ODE system

Abstract

A coupled system of an ordinary differential equation (ODE) and a heat partial differential equation (PDE) with spatially varying coefficients is discussed. By using the PDE backstepping method, the state-feedback stabilizing controller is explicitly constructed with the assumptions (x) P [ x ] n and (x) C [ 0, l ] ∞, respectively. The closed-loop system is proved to be exponentially stable by this controller. A simulation example is presented to illustrate the effectiveness of the proposed method.