REGIONAL EXPONENTIAL GENERAL OBSERVABILITY IN DISTRIBUTED PARAMETER SYSTEMS

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

Regional Boundary Asymptotic Gradient Full-Order Observer in Distributed Parabolic Systems

The purpose of this paper is to explore the concept of the regional boundary asymptotic gradient full order observer (RBAGFO-observer) in connection with the characterizations of sensors structures. Then, we present various results related to different types of measurements, domains and boundary conditions for distributed parameter systems (DPSS) in parabolic systems problem.  The considered approach of this work is derived from Luenberger observer theory which is enable to estimate asymptotically the state gradient of the original system on a sub-region of the domain boundary  in order that the RBAGFO-observability notion to be achieved. We also show that there exists a dynamical system for the considered system is not BAGFO-observer in the usual sense, but it may be regional RBAGFO-observer

Quasi-Compactness in Quasi-Banach Spaces

Quasi-compactness in a quasi-Banach space for the sequence space Lp, p< 0 < p <1 has been introduced based on the important extension of Milman's reverse Brunn-Minkowiski inequality by Bastero et al. in 1995. Moreover, Many interesting results connected with quasi-compactness and quasi-completeness in a quasi-normed space, Lp for 0 < p < 1 have been explored. Furthermore, we have shown that, the quasi-normed space under  which condition is a quasi Banach space. Also, we have shown that the space if it is quasi-compact in quasi normed space then it is  quasi Banach  space and the converse is not true. Finally, a sufficient condition of the existence for a quasi-compact operator from Lp -> Lp has been presented and analyzed

Regional Boundary Gradient Strategic Sensors Characterizations

The purpose of this paper is to characterize regional boundary gradient strategic sensors notions for different cases of regional boundary gradient observation to be achieved. Then, the characterizations based on how to a cross from internal gradient region to the boundary gradient region. Thus, the obtained results are applied in two dimensional linear infinite distributed systems in Hilbert space where the dynamics are governed by strongly continuous semi-group. Moreover, we give the relation between the regional gradient observability on a subregion  of the spatial domain  with the regional boundary gradient observability on a subregion  of the boundary  of . Finally, sufficient conditions of regional boundary gradient strategic sensors notions are explored, analyzed and discussed in connection with the regional boundary gradient of exact (weak) observability, positive definite observability operator and rank conditions