State Feedback Stabilization for a Class of Nonlinear PDE-ODE Cascade Systems

This study investigates stabilization via state feedback for an interconnected system consisting of a heat partial differential equation (PDE) subsystem and a nonlinear ordinary differential equation (ODE) subsystem. A novel feedback controller is constructed through a low-gain methodology, guaranteeing exponential stabilization of the composite system in the global sense. Rigorous stability analysis utilizing Lyapunov function techniques is complemented by systematic computational experiments, with quantitative results substantiating the efficacy of the developed control framework.