ABSTRACT In the present paper, we deal with the linear infinite dimensional systems in a Hilbert ... more ABSTRACT In the present paper, we deal with the linear infinite dimensional systems in a Hilbert space, where the dynamics of the system is governed by strongly continuous semi-group. Then, we examine the concept of regional gradient observability in connection with the structures of sensors on time finite horizon. Thus, the aim of this paper is to extend these results to the case of infinite time horizon. We explore the concept of regional gradient detectability in connection with the strategic gradient sensors. Furthermore, we consider two dimensional systems and the specific results related to some applications of sensors structures and G-observer.
The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state ... more The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state space system of this model as mathematical model. Moreover, we present some definitions and results which is described some concepts of linear control system analysis related to this problem. More precisely, the sufficient conditions which characterize the observability notion of linear dynamical controlled system are presented and discussed. Finally, we prove that, the electrical cardiography model is completely observable system over finite time.
The main objective of this paper is to study the concept of dependency and introduce a new subcla... more The main objective of this paper is to study the concept of dependency and introduce a new subclass linked to derivatives of higher order for polyvalent functions with a different operator. Thus, the results were important it was obtained with respect to different types of some geometric properties of which coefficient estimate, distortion and growth bounds, radii of starlikeness, convexity, and close-to-convex.
The main purpose of this paper is to study and characterize the existing of general asymptotic re... more The main purpose of this paper is to study and characterize the existing of general asymptotic regional gradient observer which observe the current gradient state of the original system in connection with gradient strategic sensors. Thus, we give an approach based to Luenberger observer theory of linear distributed parameter systems which is enabled to determinate asymptotically regional gradient estimator of current gradient system state. More precisely, under which condition the notion of asymptotic regional gradient observability can be achieved. Furthermore, we show that the measurement structures allows the existence of general asymptotic regional gradient observer and we give a sufficient condition for such asymptotic regional gradient observer in general case. We also show that, there exists a dynamical system for the considered system is not general asymptotic gradient observer in the usual sense, but it may be general asymptotic regional gradient observer. Then, for this pu...
The aim of this chapter is to introduce the concept of regional boundary exponential reduced obse... more The aim of this chapter is to introduce the concept of regional boundary exponential reduced observability in connection with the sensors characterizations on a sub-region on boundary of the considered domain boundary. More precisely, we explore the original results devoted to this concept in linear dynamical systems which is generated by a strongly continuous semi-group in Hilbert space of order one. Thus, the existence of sufficient conditions is presented and examined for regional boundary exponential reduced estimator in parabolic infinite dimensional systems. Finally, we apply these results to the exchange systems with various strategic sensors.
In this paper, a linear infinite dimensional distributed systems in a Hilbert space has been disc... more In this paper, a linear infinite dimensional distributed systems in a Hilbert space has been discussed and analyzed where the dynamics of system is governed by strongly continuous semi-groups. The characterizations of regional strategic sensors have been given and tackled for different cases of regional observability. Furthermore, the results so obtained are applied to two-dimensional systems. Various cases of sensors are considered and analyzed. Also, the authors show that, the existent of a sensor for the diffusion system is not strategic in the usual sense, but it may be regionally strategic of this system.
The main object of the present paper is to, introduce the. class of meromorphic univalent functio... more The main object of the present paper is to, introduce the. class of meromorphic univalent functions Involving! hypergeomatrc function .We obtain~ some interesting geometric properties according to coefficient inequality , growth and distortion theorems , radii of starlikeness and convexity for the" functions in our subclass.
This paper is aimed at investigating and introducing the main results regarding the concept of Re... more This paper is aimed at investigating and introducing the main results regarding the concept of Regional Boundary Gradient Strategic Sensors (RBGS-sensors the in Diffusion Distributed Parameter Systems (DDP-Systems . Hence, such a method is characterized by Parabolic Differential Equations (PDEs in which the behavior of the dynamic is created by a Semigroup ( of Strongly Continuous type (SCSG in a Hilbert Space (HS) . Additionally , the grantee conditions which ensure the description for such sensors are given respectively to together with the Regional Boundary Gradient Observability (RBG-Observability can be studied and achieved . Finally , the results gotten are applied to different situations with altered sensors positions are undertaken and examined.
The main aim of the present work is to introduce the class of multivalent harmonic functions defi... more The main aim of the present work is to introduce the class of multivalent harmonic functions defined by the general integral operator. Thus, We get some geometric properties, like coefficients estimate, extreme point and distortion theorem, convolution property, radii of starlikeness, and convexity.
The purpose of this paper is to introduce the notion of regional boundary asymptotic gradient red... more The purpose of this paper is to introduce the notion of regional boundary asymptotic gradient reduced order observer (Γ*AGRO-observer) in distributed parameter systems. More precisely, we explore and discuss the existing of this approach in which estimates a considered sub-region Γ* for the considered domain boundary. Thus, we show that the approach is enables to build the unknown part of the state gradient when the output function gives part of information about the region state. Furthermore, the characterization of this notion depend on regional boundary gradient strategic sensors (RBG-strategic sensors) concept in order that regional boundary asymptotic gradient reduced order observability (Γ*AGRO-observability) to be achieved and analyzed. Finally, an application is presented to various situations of strategic sensors for internal case.
The main objective of this paper is to study the problem of regional boundary asymptotic gradient... more The main objective of this paper is to study the problem of regional boundary asymptotic gradient full order observer (Γ*AGFO-observer) in link with the structures of sensors and actuators. Important results have been obtained related to diverse kinds of measurements and controls, of domains and boundary conditions. It has been shown that the structures of measurements and feedback controls allow the existence of Γ*AGFO-observer in order to achieve regional boundary gradient closed loop control system (Γ*AGFO-system). It has also been found that there is a dynamical system which does not represent the observer in the usual sense, but it could be interpreted as a regional observer.
The aim of this paper is to extend the notion of general asymptotic regional gradient observer (G... more The aim of this paper is to extend the notion of general asymptotic regional gradient observer (G A R G-observer) to the reduced order case. More precisely, we study and discuss the existing of this approach in a sub-region of the considered domain. Thus, we show that the approach is enables to estimate the unknown part of the state gradient when the output function gives part of information about the region state in ω. The characterization of this notion depend on regional gradient strategic sensors (R G S-sensor) concept in order that asymptotic regional gradient reduced-order observability (A R G R O-observability) to be achieved and analyzed. An application presented to various situation cases of strategic sensors.
The main idea of this paper is to explore and present the original results related to the notion ... more The main idea of this paper is to explore and present the original results related to the notion of regional boundary gradient strategic sensors in distributed parameter system for Neumann problem. Thus, this systems is described by parabolic state space partial differential equations where the dynamic is governed by strongly continuous semi-group in Hilbert space. In addition, we give the sufficient conditions which are guaranteed the characterizations for such sensors in order that regional boundary approximately gradient observability can be achieved and proved. The obtained results are applied to two-dimensional circular in a part of considered system domain with various cases of sensors locations are tackled and studied.
The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state ... more The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state space system of this model as mathematical model. Moreover, we present some definitions and results which is described some concepts of linear control system analysis related to this problem. More precisely, the sufficient conditions which characterize the observability notion of linear dynamical controlled system are presented and discussed. Finally, we prove that, the electrical cardiography model is completely observable system over finite time .
In the present paper, the characterizations of regional gradient strategic sensors notions have b... more In the present paper, the characterizations of regional gradient strategic sensors notions have been given for different cases of regional gradient observability. The results obtained are applied to two dimensional linear infinite distributed system in Hilbert space where the dynamic is governed by strongly continuous semi-group. Various cases of regional strategic sensors are considered and analyzed in connection with regional gradient strategic sensors concepts. Also, we show that there is a various sensors which are not gradient strategic in usual sense for the considered systems, but may be regionally gradient strategic of this system.
In this paper the Regional Gradient Detectability ( R G – Detectability) based on Sensors and Act... more In this paper the Regional Gradient Detectability ( R G – Detectability) based on Sensors and Actuators Structures (SAS). So, we reflect a class of Distributed Parameter Systems (DPSs) in Sobolev Space (SS) such that the dynamics of the system is ruled by Strongly Continuous SemiGroup (SCSS). More accurately, we discover numerous outcomes connected with diverse types of structures with a view to accomplish that Regional Gradient Observability ( R G – Observabilityty) notion. Therefore, we establish that, the existence of Gradient Detectable System (GD – System) is not realized in general case, but it perhaps Regionally Gradient Detectable System (RG – Detctable System).
The purpose of this paper is to deals with the problem of regional boundary asymptotic gradient f... more The purpose of this paper is to deals with the problem of regional boundary asymptotic gradient full order observer (-observer) concept by using internal regional case. Thus, we study the relation between this notion and the corresponding asymptotic detectability and sensors. More precisely, various important results have been examined and explored concern an extension of an approach which enables to reconstruct the gradient of current state from internal region. In addition, it has been shown that the characterization of -observability under which conditions to be achieved. Finally, we have illustrate that there is a dynamical system which does not represent the observer in the usual sense, but it could be interpreted as a -observer.
The purpose of this paper is to explore the concept of the regional boundary asymptotic gradient ... more 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.
ABSTRACT In the present paper, we deal with the linear infinite dimensional systems in a Hilbert ... more ABSTRACT In the present paper, we deal with the linear infinite dimensional systems in a Hilbert space, where the dynamics of the system is governed by strongly continuous semi-group. Then, we examine the concept of regional gradient observability in connection with the structures of sensors on time finite horizon. Thus, the aim of this paper is to extend these results to the case of infinite time horizon. We explore the concept of regional gradient detectability in connection with the strategic gradient sensors. Furthermore, we consider two dimensional systems and the specific results related to some applications of sensors structures and G-observer.
The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state ... more The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state space system of this model as mathematical model. Moreover, we present some definitions and results which is described some concepts of linear control system analysis related to this problem. More precisely, the sufficient conditions which characterize the observability notion of linear dynamical controlled system are presented and discussed. Finally, we prove that, the electrical cardiography model is completely observable system over finite time.
The main objective of this paper is to study the concept of dependency and introduce a new subcla... more The main objective of this paper is to study the concept of dependency and introduce a new subclass linked to derivatives of higher order for polyvalent functions with a different operator. Thus, the results were important it was obtained with respect to different types of some geometric properties of which coefficient estimate, distortion and growth bounds, radii of starlikeness, convexity, and close-to-convex.
The main purpose of this paper is to study and characterize the existing of general asymptotic re... more The main purpose of this paper is to study and characterize the existing of general asymptotic regional gradient observer which observe the current gradient state of the original system in connection with gradient strategic sensors. Thus, we give an approach based to Luenberger observer theory of linear distributed parameter systems which is enabled to determinate asymptotically regional gradient estimator of current gradient system state. More precisely, under which condition the notion of asymptotic regional gradient observability can be achieved. Furthermore, we show that the measurement structures allows the existence of general asymptotic regional gradient observer and we give a sufficient condition for such asymptotic regional gradient observer in general case. We also show that, there exists a dynamical system for the considered system is not general asymptotic gradient observer in the usual sense, but it may be general asymptotic regional gradient observer. Then, for this pu...
The aim of this chapter is to introduce the concept of regional boundary exponential reduced obse... more The aim of this chapter is to introduce the concept of regional boundary exponential reduced observability in connection with the sensors characterizations on a sub-region on boundary of the considered domain boundary. More precisely, we explore the original results devoted to this concept in linear dynamical systems which is generated by a strongly continuous semi-group in Hilbert space of order one. Thus, the existence of sufficient conditions is presented and examined for regional boundary exponential reduced estimator in parabolic infinite dimensional systems. Finally, we apply these results to the exchange systems with various strategic sensors.
In this paper, a linear infinite dimensional distributed systems in a Hilbert space has been disc... more In this paper, a linear infinite dimensional distributed systems in a Hilbert space has been discussed and analyzed where the dynamics of system is governed by strongly continuous semi-groups. The characterizations of regional strategic sensors have been given and tackled for different cases of regional observability. Furthermore, the results so obtained are applied to two-dimensional systems. Various cases of sensors are considered and analyzed. Also, the authors show that, the existent of a sensor for the diffusion system is not strategic in the usual sense, but it may be regionally strategic of this system.
The main object of the present paper is to, introduce the. class of meromorphic univalent functio... more The main object of the present paper is to, introduce the. class of meromorphic univalent functions Involving! hypergeomatrc function .We obtain~ some interesting geometric properties according to coefficient inequality , growth and distortion theorems , radii of starlikeness and convexity for the" functions in our subclass.
This paper is aimed at investigating and introducing the main results regarding the concept of Re... more This paper is aimed at investigating and introducing the main results regarding the concept of Regional Boundary Gradient Strategic Sensors (RBGS-sensors the in Diffusion Distributed Parameter Systems (DDP-Systems . Hence, such a method is characterized by Parabolic Differential Equations (PDEs in which the behavior of the dynamic is created by a Semigroup ( of Strongly Continuous type (SCSG in a Hilbert Space (HS) . Additionally , the grantee conditions which ensure the description for such sensors are given respectively to together with the Regional Boundary Gradient Observability (RBG-Observability can be studied and achieved . Finally , the results gotten are applied to different situations with altered sensors positions are undertaken and examined.
The main aim of the present work is to introduce the class of multivalent harmonic functions defi... more The main aim of the present work is to introduce the class of multivalent harmonic functions defined by the general integral operator. Thus, We get some geometric properties, like coefficients estimate, extreme point and distortion theorem, convolution property, radii of starlikeness, and convexity.
The purpose of this paper is to introduce the notion of regional boundary asymptotic gradient red... more The purpose of this paper is to introduce the notion of regional boundary asymptotic gradient reduced order observer (Γ*AGRO-observer) in distributed parameter systems. More precisely, we explore and discuss the existing of this approach in which estimates a considered sub-region Γ* for the considered domain boundary. Thus, we show that the approach is enables to build the unknown part of the state gradient when the output function gives part of information about the region state. Furthermore, the characterization of this notion depend on regional boundary gradient strategic sensors (RBG-strategic sensors) concept in order that regional boundary asymptotic gradient reduced order observability (Γ*AGRO-observability) to be achieved and analyzed. Finally, an application is presented to various situations of strategic sensors for internal case.
The main objective of this paper is to study the problem of regional boundary asymptotic gradient... more The main objective of this paper is to study the problem of regional boundary asymptotic gradient full order observer (Γ*AGFO-observer) in link with the structures of sensors and actuators. Important results have been obtained related to diverse kinds of measurements and controls, of domains and boundary conditions. It has been shown that the structures of measurements and feedback controls allow the existence of Γ*AGFO-observer in order to achieve regional boundary gradient closed loop control system (Γ*AGFO-system). It has also been found that there is a dynamical system which does not represent the observer in the usual sense, but it could be interpreted as a regional observer.
The aim of this paper is to extend the notion of general asymptotic regional gradient observer (G... more The aim of this paper is to extend the notion of general asymptotic regional gradient observer (G A R G-observer) to the reduced order case. More precisely, we study and discuss the existing of this approach in a sub-region of the considered domain. Thus, we show that the approach is enables to estimate the unknown part of the state gradient when the output function gives part of information about the region state in ω. The characterization of this notion depend on regional gradient strategic sensors (R G S-sensor) concept in order that asymptotic regional gradient reduced-order observability (A R G R O-observability) to be achieved and analyzed. An application presented to various situation cases of strategic sensors.
The main idea of this paper is to explore and present the original results related to the notion ... more The main idea of this paper is to explore and present the original results related to the notion of regional boundary gradient strategic sensors in distributed parameter system for Neumann problem. Thus, this systems is described by parabolic state space partial differential equations where the dynamic is governed by strongly continuous semi-group in Hilbert space. In addition, we give the sufficient conditions which are guaranteed the characterizations for such sensors in order that regional boundary approximately gradient observability can be achieved and proved. The obtained results are applied to two-dimensional circular in a part of considered system domain with various cases of sensors locations are tackled and studied.
The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state ... more The aim of this paper, is to study electrical cardiography problem. Thus, we construct the state space system of this model as mathematical model. Moreover, we present some definitions and results which is described some concepts of linear control system analysis related to this problem. More precisely, the sufficient conditions which characterize the observability notion of linear dynamical controlled system are presented and discussed. Finally, we prove that, the electrical cardiography model is completely observable system over finite time .
In the present paper, the characterizations of regional gradient strategic sensors notions have b... more In the present paper, the characterizations of regional gradient strategic sensors notions have been given for different cases of regional gradient observability. The results obtained are applied to two dimensional linear infinite distributed system in Hilbert space where the dynamic is governed by strongly continuous semi-group. Various cases of regional strategic sensors are considered and analyzed in connection with regional gradient strategic sensors concepts. Also, we show that there is a various sensors which are not gradient strategic in usual sense for the considered systems, but may be regionally gradient strategic of this system.
In this paper the Regional Gradient Detectability ( R G – Detectability) based on Sensors and Act... more In this paper the Regional Gradient Detectability ( R G – Detectability) based on Sensors and Actuators Structures (SAS). So, we reflect a class of Distributed Parameter Systems (DPSs) in Sobolev Space (SS) such that the dynamics of the system is ruled by Strongly Continuous SemiGroup (SCSS). More accurately, we discover numerous outcomes connected with diverse types of structures with a view to accomplish that Regional Gradient Observability ( R G – Observabilityty) notion. Therefore, we establish that, the existence of Gradient Detectable System (GD – System) is not realized in general case, but it perhaps Regionally Gradient Detectable System (RG – Detctable System).
The purpose of this paper is to deals with the problem of regional boundary asymptotic gradient f... more The purpose of this paper is to deals with the problem of regional boundary asymptotic gradient full order observer (-observer) concept by using internal regional case. Thus, we study the relation between this notion and the corresponding asymptotic detectability and sensors. More precisely, various important results have been examined and explored concern an extension of an approach which enables to reconstruct the gradient of current state from internal region. In addition, it has been shown that the characterization of -observability under which conditions to be achieved. Finally, we have illustrate that there is a dynamical system which does not represent the observer in the usual sense, but it could be interpreted as a -observer.
The purpose of this paper is to explore the concept of the regional boundary asymptotic gradient ... more 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.
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