Feedback Control for Nonlinear ODE–PDE–ODE-Coupled Systems

In this article, we are devoted to the global stabilization for ordinary differential equation (ODE)-parabolic partial differential equation (PDE)-ODE-coupled systems subject to spatially varying coefficient, where a nonlinear ODE is located at the driving end and a linear ODE is located at the other end. By means of infinite-dimensional and finite-dimensional backstepping transformations, both state-feedback and output-feedback controllers are established to assure the global exponential stability of the resulting closed-loop system. Besides, the boundedness and exponential convergence of the controllers are also investigated. Finally, the availability of the theoretical results is illustrated by simulation data.