Abstract
The purpose of this paper is to explore the concept of regional exponential general observability for a class of distributed parameter systems, in connection with the regional strategic sensors. Then, we give characterization of the strategic sensors in order that exponential regional general observability can be achieved. Furthermore, we apply these results to one and two dimensional systems, and various cases of sensors are considered and discussed. We also show that there exists a dynamical system for diffusion system is not exponentially general observable in the usual sense, but it may be regionally exponentially general observable.
Highlights
The theory of observer was introduced by Luenberger (1966) [26] and has been generalized to system described by semigroup operators governed by partial differential infinite dimensional equations in Hilbert state space (Gressang and Lamont 1975) [25]
The aim of this paper is to extend some results related to regional exponential observability and strategic sensor to the general case as in ref.s [3, 7]
We present the sufficient condition of regional exponential general observability concept in the following result
Summary
The theory of observer was introduced by Luenberger (1966) [26] and has been generalized to system described by semigroup operators governed by partial differential infinite dimensional equations in Hilbert state space (Gressang and Lamont 1975) [25]. The exponential observability is related to the possibility to estimate the state from knowledge of the state estimator system and output function [15]. The concept of actuators and sensors are introduced and applied to the controllability, observability and exponential estimator of systems described by partial differential equations as in [16,17]. The aim of this paper is to extend some results related to regional exponential observability and strategic sensor to the general case as in ref.s [3, 7]. The outline of this paper is organized as follows: Section 2 is related to define the problem statement, regional strategic sensors, definitions and characterizations.
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