Sensors structures and regional exponential detectability

In this paper, we deal with linear infinite dimensional systems in a Hilbert space where the dynamics of the system are governed by strongly continuous semi-groups. We study the concept of exponential regional detectability in connection with the structures of sensors for a class of parabolic distributed parameter systems. For different sensors structures, we give the characterization of the exponential regional detectability. Furthermore, we apply these results to a regional observer for a diffusion systems.