Stabilization of a coupled PDE-ODE system by boundary control

A coupled system of an ODE and a diffusion PDE is considered in this paper. Special techniques as well as the method of PDE backstepping are employed to construct controllers. Through transforming the system into an exponentially stable PDE-ODE cascade, a state feedback boundary controller is established. Moreover, an observer for anti-collocated setup is proposed, and the observer error is shown to exponentially converge to zero, then an output feedback boundary controller is obtained. For a scalar coupled PDE-ODE system, the boundary controller and observer, as well as the solution of the closed-loop system are given explicitly.