Regional exponential general observability in diffusion problem

TL;DR

This paper extends the concept of regional exponential general observability to diffusion systems with Neumann boundary conditions, enabling state reconstruction in sub-regions and highlighting sensor design implications.

Contribution

It introduces the notion of regional exponential general observability for diffusion systems with Neumann boundary conditions, including sensor characterization and conditions for regional observability.

Findings

Regional exponential observability can be achieved in sub-regions of diffusion systems.

Sensor configurations are crucial for regional observability.

Some systems are not globally observable but are regionally observable.

Abstract

The aim of this paper is to extend the concept of regional exponential general observability to the case of Neumann boundary conditions problem in diffusion system. More precisely, for linear distributed parameter diffusion systems, we show that the sensors characterizations allow to reconstruct the regional exponential state in a sub-region of the considered systems domain. Moreover, various interesting results associated with the choice of sensors are given and illustrated in specific situations in order regional exponential general observability notion to be achieved. Finally, we also show that, there exists a dynamical system for diffusion system is not exponential general observable in the usual sense, but it may be regional exponential general observable.