Abstract
In this paper, we study the finite-dimensional stabilization problem of the cascade of the one-dimensional transport-diffusion process with an unstable ODE plant, where it is assumed that the ODE plant is controllable and observable and the plant is connected with the transport-diffusion process through a filter. The input to the whole system is only Neumann boundary input to the transport-diffusion process, and the outputs are the data at the boundary of process domain and the output of the ODE plant. We use the previous result that the one-dimensional transport-diffusion process can be formulated as a system with Aγ-bounded output operator. In this paper, it is proved that the finite-dimensional model of the whole system is controllable and observable when the filter is a Residual Mode Filter (RMF). This fact enables us to construct a finite-dimensional stabilizing controller by using an RMF approach. The point that the output from the same RMF is used in the two parts features this paper.
