Stabilization for a class of delayed coupled PDE-ODE systems with boundary control

A class of coupled PDE-ODE systems with delays at the input and two-directional interconnection at the interfaces (one single point) is discussed in this paper. Exponential stability in the sense of the corresponding norms for the original closed-loop system with the derived controller is obtained by finally transforming the system into an exponentially stable PDEs-ODE cascade with a boundary feedback backstepping controller, and the result is also rigidly proved.