Output Feedback Stabilization of Coupled Reaction-Diffusion Processes with Constant Parameters

The problem of output feedback boundary stabilization is considered for $n$ coupled plants, distributed over the one-dimensional spatial domain [0,1] where they are governed by linear reaction-diffusion partial differential equations (PDEs). All plants have constant parameters and each is equipped with its own scalar boundary control input, acting at one end of the domain. First, a state feedback law is designed to exponentially stabilize the closed-loop system with an arbitrarily fast convergence rate. Then, collocated and anticollocated observers are designed, using a single boundary measurement for each plant. The exponential convergence of the observed state towards the actual one is demonstrated for both observers, with a convergence rate that can be made as fast as desired. Finally, the state feedback controller and the preselected, either collocated or anticollocated, observer are coupled together to yield an output feedback stabilizing controller. The distinct treatments are proposed separately fo...