Stabilization of coupled linear plant and reaction-diffusion process

Boundary control to stabilize a system of coupled linear plant and reaction-diffusion process is considered. Backstepping transformations with a kernel function and a vector-valued function are introduced to design control laws. For the situation without heat resource, the kernel function and the vector-valued function of the transformation are obtained, and an explicit control law is established, and simulation results are presented through figures. For the general situation with heat resource, the existence of the kernel and the vector-valued function of the transformations is shown, and an control law is derived. Stability of the closed loops is achieved for both the situations.