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The aim of this paper is study and explore the notion of the regional boundary gradient detectability in connection with the choice of strategic gradient sensors on sub-region of the considered system domain boundary. More precisely, the principal reason behind introducing this notion is that the possibility to design a dynamic system (may be called regional boundary gradient observer) which enable to estimate the unknown system state gradient. Then for linear infinite dimensional systems in a Hilbert space, we give various new results related with different measurements. In addition, we provided a description of the regional boundary gradient strategic sensors for completion the regional boundary gradient observability and regional boundary gradient detectability. Finally, we present and illustrate some applications of sensors structures which relate by regional boundary gradient detectability in diffusion distributed parameter systems.

Regional Boundary Gradient Detectability in Distributed Parameter Systems