Neumann boundary control of a coupled transport-diffusion system with boundary observation

We study the Neumann boundary stabilization problem of a coupled transport-diffusion system in the case where the observation is done at the boundary. In the recent paper of Sano and Nakagiri [H. Sano, S. Nakagiri, Stabilization of a coupled transport-diffusion system with boundary input, J. Math. Anal. Appl. 363 (2010) 57-72], we treated the stabilization problem for the case with Neumann boundary control and distributed observation. The novelty of this paper is the formulation of the boundary observation equation in a Hilbert space. We have an interesting result of its being expressed by using an -bounded operator with . Moreover, it is shown that a reduced-order model with a finite-dimensional state variable is controllable and observable. This means that one can always construct a finite-dimensional stabilizing controller for the original infinite-dimensional system by using a residual mode filter (RMF) approach.