Abstract
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 exponential gradient strategic sensors for completion the regional boundary exponential gradient observability and regional boundary exponential gradient detectability. Finally, we present and illustrate the some applications of sensors structures which relate by regional boundary exponential gradient detectability in diffusion distributed parameter systems.
Highlights
Many real problems in the sensors and detectability of distributed parameter systems can be reformulated as problems of infinite dimensional systems in a domain Ω [1,2,3]
The purpose of this paper is to study and investigate the concept of regional boundary gradient detectability by using the choice of sensors
We will give some definitions which will be used to explain the notion of regional boundary gradient observability and detectability in (H1⁄2 (Γ))n
Summary
Many real problems in the sensors and detectability of distributed parameter systems can be reformulated as problems of infinite dimensional systems in a domain Ω [1,2,3]. The concept of regional and regional boundary analysis has been introduced by El Jai, Zerrik, Al-Saphory et al, for finite time horizon [9,10,11,12,13] and for infinite time horizon [14,15,16] This concept which is given important tool to solve many problems in real world not in total domain of the considered system state but in sub -region of the domain or of the boundary [17,18,19]. Section tackles the relation between regional boundary detectability of state gradient and regional boundary observer
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