Abstract
The regional exponential reduced observability concept in the presence for linear dynamical systems is addressed for a class of distributed parameter systems governed by strongly continuous semi group in Hilbert space. Thus, the existence of necessary and sufficient conditions is established for regional exponential reduced estimator in parabolic infinite dimensional systems. More precisely, the introduced approach is developed by using the decomposed system and reduced system in connection with various new concepts of (stability, detectability, estimator, observability and strategic sensors). Finally, we also show that there exists a dynamical system for two-phase exchange system described by the coupled parabolic equations is not exponentially reduced observable in usual sense, but it may be regionally exponentially reduced observable.
Highlights
NTRODUCTIONOne of the most important concepts in infinite dimensional systems analysis is observability concept
One of the most important concepts in infinite dimensional systems analysis is observability concept. Many researches of these concept included the notion of exponential observer( estimator), where Luenberger introduced this notion for finite dimensional systems [22], and has been generalized to infinite dimensional systems described by strongly continuous linear semi-group operators by Gressang and Lamont [20]
New concept of regional analysis for a class of distributed parameter systems was extended by Al-Saphory and El Jai et al as in ref.s [1,2,3,4,5,6,7, 18, 16, 25,26,27,28,29]
Summary
One of the most important concepts in infinite dimensional systems analysis is observability concept. We introduce and study the notion of exponential regional reduced state observability in a given region ω of the domain Ω. The scenario described by (Figure 1) below, one is interested in estimating the state in the green zone rather than in the entire space [12] This problem falls into a class of so-called regional observation and estimation problem introduced by Al-Saphory and El-Jai and their workers as in [1,2,3,4,5,6,7, 25,26,27,28,29]. We illustrate applications with different domains and circular strategic sensors of two-phase exchange systems
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