Sensors structures and regional detectability of parabolic distributed systems

In this paper, we deal with the linear infinite dimensional systems in a Hilbert space where the dynamics of the system is governed by strongly continuous semi-groups. We study the concept of asymptotic (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 asymptotic (exponential) regional detectability in order that asymptotic (exponential) regional observability be achieved. Furthermore, we apply these results to the regional observer for distributed parameter diffusion systems.