Control of Cascaded System of ODE/Wave PDE with Nonlocal Term

We consider the cascaded system of nonlinear ordinary differential equation (ODE) and wave partial differential equation (PDE) with nonlocal term. A predictor controller is designed for the cascaded system. It can be proved that the closed-loop system is globally asymptotically stable. Stability analysis of the closed-loop system is based on the infinite-dimensional backstepping transformation and an appropriate Lyapunov functional.