References of "Ndoye, Ibrahima 40080165"
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See detailDesign of Unkown Input Fractional-Order Observers for Fractional-Order Systems
Ndoye, Ibrahima UL; Darouach, Mohamed; Voos, Holger UL et al

in International Journal of Applied Mathematics & Computer Science (2013), 23(3), 491-500

This paper considers a method to design fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. The conditions for the existence of these observers are given ... [more ▼]

This paper considers a method to design fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. The conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of the fractional-order observer errors with the fractional-order \alpha satisfying 0<\alpha<2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach where the fractional-order \alpha belongs to 1<\alpha<2 and 0<\alpha<1 respectively. The stability analysis of the fractional-order error system is completed and it is shown that the fractional-order observers are as stable as their integer-order counterpart and guarantee better convergence of the estimation error. [less ▲]

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See detailRobust stabilization of uncertain descriptor fractional-order systems
Ndoye, Ibrahima UL; Darouach, Mohamed; Zasadzinski, Michel et al

in Automatica (2013)

This paper presents sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional order α satisfying 0<\alpha<2. The results are ... [more ▼]

This paper presents sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional order α satisfying 0<\alpha<2. The results are obtained in terms of linear matrix inequalities. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in the state matrix. A necessary and sufficient condition for the normalization of uncertain descriptor fractional-order systems is given via linear matrix inequality (LMI) formulation. The state feedback control to robustly stabilize such uncertain descriptor fractional-order systems with the fractional order \alpha belonging to 0</alpha<2 is derived. Two numerical examples are given to demonstrate the applicability of the proposed approach. [less ▲]

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See detailObserver-Based Approach for Fractional-Order Chaotic Synchronization and Communication
Ndoye, Ibrahima UL; Darouach, Mohamed; Voos, Holger UL

in European Control Conference (ECC), Switzerland, July 17-19, 2013 (2013)

This paper presents a method based on the state observer design for constructing a chaotically synchronized systems. Fractional-order direct Lyapunov theorem is used to derive the closed-loop asymptotic ... [more ▼]

This paper presents a method based on the state observer design for constructing a chaotically synchronized systems. Fractional-order direct Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer-based controller are obtained in terms of linear matrix inequalities (LMIs) formulation. The proposed approach is then applied to secure communications. The method combines chaotic masking and chaotic modulation, where the information signal is injected into the transmitter and simultaneously transmitted to the receiver. Chaotic synchronization and chaotic communication are achieved simultaneously via a state observer design technique. An numerical fractional-order chaotic Lorenz system is given to demonstrate the applicability of the proposed approach. [less ▲]

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See detailH-infinity Static Output Feedback Control for a Fractional-Order Glucose-Insulin System
Ndoye, Ibrahima UL; Voos, Holger UL; Darouach, Mohamed et al

in 6th Workshop on Fractional Differentiation and Its Applications. Part of 2013 IFAC Joint Conference SSSC, TDS and FDA (2013), Grenoble, February 4-6, 2013 (2013)

This paper presents the H-infinity static output feedback control of nonlinear fractional-order glucose-insulin systems. In this paper, it is an attempt to incorporate fractional-order into the ... [more ▼]

This paper presents the H-infinity static output feedback control of nonlinear fractional-order glucose-insulin systems. In this paper, it is an attempt to incorporate fractional-order into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to show, how the order of a fractional di erential system a ects the dynamics of system in the presence of meal disturbance. A static output feedback control is considered for the problem. Su fficient conditions are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order \alpha belongs to 0<\alpha<1. Finally, numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are as stable as their integer-order counterpart in the presence of exogenous glucose infusion or meal disturbance. [less ▲]

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See detailObserver-Based Approach for Fractional-Order Chaotic Synchronization and Secure Communication
Ndoye, Ibrahima UL; Voos, Holger UL; Darouach, Mohamed

in IEEE Journal on Emerging and Selected Topics in Circuits and Systems (2013), 3(3), 442-450

This paper presents a method based on the state observer design for constructing a chaotically synchronized systems. Fractional-order direct Lyapunov theorem is used to derive the closed-loop asymptotic ... [more ▼]

This paper presents a method based on the state observer design for constructing a chaotically synchronized systems. Fractional-order direct Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer-based controller are obtained in terms of linear matrix inequalities (LMIs) formulation. The proposed approach is then applied to secure communications. The method combines chaotic masking and chaotic modulation, where the information signal is injected into the transmitter and simultaneously transmitted to the receiver. Chaotic synchronization and chaotic communication are achieved simultaneously via a state observer design technique. The fractional-order chaotic Lorenz and Lü systems are given to demonstrate the applicability of the proposed approach. [less ▲]

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See detailObserver-Based Approach for Fractional-Order Chaotic Synchronization and Communication
Ndoye, Ibrahima UL; Darouach, Mohamed; Voos, Holger UL

in European Control Conference (ECC), July 17-19, 2013, Switzerland (2013)

This paper presents a method based on the state observer design for constructing a chaotically synchronized systems. Fractional-order direct Lyapunov theorem is used to derive the closed-loop asymptotic ... [more ▼]

This paper presents a method based on the state observer design for constructing a chaotically synchronized systems. Fractional-order direct Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer-based controller are obtained in terms of linear matrix inequalities (LMIs) formulation. The proposed approach is then applied to secure communications. The method combines chaotic masking and chaotic modulation, where the information signal is injected into the transmitter and simultaneously transmitted to the receiver. Chaotic synchronization and chaotic communication are achieved simultaneously via a state observer design technique. An numerical fractional-order chaotic Lorenz system is given to demonstrate the applicability of the proposed approach. [less ▲]

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See detailFractional-Order Observers Design for Fractional-Order Systems with Unknown Inputs
Ndoye, Ibrahima UL; Darouach, Mohamed; Zasadzinski, Michel

in 2nd International Conference on Systems and Control, Morocco, June 20-22, 2012 (2012)

This paper considers a method to design the functional observers for continuous-time linear fractional-order systems with unknown inputs. The conditions for the existence of these observers are given ... [more ▼]

This paper considers a method to design the functional observers for continuous-time linear fractional-order systems with unknown inputs. The conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of observers with the fractional-order satisfying 0<\alpha<2 are derived in terms of linear matrix inequalities formulation. Two numerical examples are given to demonstrate the applicability of the proposed approach where the fractional-order belonging to 1<\alpha<2 and 0<\alpha<1 respectively. [less ▲]

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See detailStatic Output Feedback Stabilization of Nonlinear Fractional-Order Glucose-Insulin System
Ndoye, Ibrahima UL; Voos, Holger UL; Darouach, Mohamed et al

in IEEE EMBS Conference on Biomedical Engineering and Sciences, Malaysia, 17th - 19th December, 2012 (2012)

Diabetes is a long-term disease during which the body's production and use of the insulin are impaired, causing glucose concentration level to increase in the bloodstream. The blood glucose dynamics is ... [more ▼]

Diabetes is a long-term disease during which the body's production and use of the insulin are impaired, causing glucose concentration level to increase in the bloodstream. The blood glucose dynamics is described using the generalized minimal model structure for the intravenously infused insulin blood glucose, which can represent a wide variety of diabetic patients. In this paper, it is an attempt to incorporate fractional-order derivative into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to determine, mathematically, how the order of a fractional differential system affects the dynamics of system. The paper presents the asymptotical stabilization problem of nonlinear fractional-order glucose insulin systems. A static output feedback control is considered for the problem. Sufficient conditions for the asymptotical stabilization of the nonlinear fractional-order glucose-insulin system are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order \alpha belonging to 0<\alpha<1. Finally, numerical simulations are carried out to illustrate our proposed results. These numerical simulations show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer-order counterpart. [less ▲]

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See detailAn Unknown Input Fractional-Order Observer Design for Fractional-Order Glucose-Insulin System
Ndoye, Ibrahima UL; Voos, Holger UL; Darouach, Mohamed et al

in IEEE EMBS Conference on Biomedical Engineering and Sciences, Malaysia, 17th - 19th December, 2012 (2012)

In this paper, we introduce fractional-order derivatives into a generalized minimal model of glucose-insulin. A fractional-order state observer is designed for estimating the structure of a blood glucose ... [more ▼]

In this paper, we introduce fractional-order derivatives into a generalized minimal model of glucose-insulin. A fractional-order state observer is designed for estimating the structure of a blood glucose-insulin with glucose rate disturbance to show the complete dynamics of the glucose-insulin system where the fractional-order \alpha belonging to 0<\alpha<1. A nonlinear fractional-order unknown input observer strategy is used where the glucose rate disturbance is considered as an unknown input to the perspective dynamical system. The developed method provides the observer estimation algorithm for a glucose-insulin system with unknown time-varying glucose rate disturbance. The stability analysis of the fractional-order error system is completed and showed that the fractional-order observer design is as stable as their integer-order counterpart and guarantees the best convergence of the estimation error. Finally, numerical simulations are given to illustrate the effectiveness of the proposed method. [less ▲]

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See detailExponential Stabilization of a Class of Nonlinear Systems : A Generalized Gronwall-Bellman Lemma Approach
Ndoye, Ibrahima UL; Zasadzinski, Michel; Darouach, Mohamed et al

in Nonlinear Analysis: Theory, Methods & Applications (2011), 74

In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall-Bellman lemma approach. The nonlinear systems under consideration can be ... [more ▼]

In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall-Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show the effectiveness of the proposed method. [less ▲]

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See detailObservers for Singular Fractional-Order Systems
Ndoye, Ibrahima UL; Darouach, Mohamed; Zasadzinski, Michel et al

in 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, FL, USA, December 12-15, 2011 (2011)

This paper considers the observers design for continuous-time singular fractional-order systems. The approach is based on the generalized Sylvester equations solutions. The conditions for the existence of ... [more ▼]

This paper considers the observers design for continuous-time singular fractional-order systems. The approach is based on the generalized Sylvester equations solutions. The conditions for the existence of these observers are given and sufficient conditions for their stability are derived in terms of linear matrix inequalities formulation. [less ▲]

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See detailRegularization and Robust Stabilization of Singular Uncertain Fractional-Order Systems
Ndoye, Ibrahima UL; Zasadzinski, Michel; Darouach, Mohamed et al

in 18th IFAC World Congress, Milano, Italy, 2011 (2011)

In this paper, robust asymptotical stabilization problem via a predictive and memoryless static feedbacks for uncertain singular fractional-order systems for the fractional-order belonging to 0<\alpha<2 ... [more ▼]

In this paper, robust asymptotical stabilization problem via a predictive and memoryless static feedbacks for uncertain singular fractional-order systems for the fractional-order belonging to 0<\alpha<2 is investigated. The parameter uncertainty is assumed to be time-invariant and norm-bounded appearing in the state matrix. Suffcient linear matrix inequalities (LMIs) conditions for regularization of uncertain singular fractional-order systems are given. Then, the predictive controller aims to regularizing the uncertain singular fractional-order systems while the memoryless state feedback is designed to stabilize the resulting regularized system. A numerical example is given to demonstrate the applicability of the proposed approach. [less ▲]

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See detailRobust Stabilization of Linear and Nonlinear Fractional-Order Systems with Nonlinear Uncertain Parameters
Ndoye, Ibrahima UL; Zasadzinski, Michel; Darouach, Mohamed et al

in 49th IEEE Conference on Decision and Control (CDC), Hilton Atlanta Hotel, Atlanta, December 15-17, 2010 (2010)

The paper presents the robust stabilization problem of linear and nonlinear fractional-order systems with nonlinear uncertain parameters. The uncertainty in the model appears in the form of combination of ... [more ▼]

The paper presents the robust stabilization problem of linear and nonlinear fractional-order systems with nonlinear uncertain parameters. The uncertainty in the model appears in the form of combination of additive perturbation and multiplicative perturbation. Sufficient conditions for robust stabilization of such linear and nonlinear fractional-order systems are presented in terms of linear matrix inequalities and using the new generalization of Gronwall-Bellman approach. [less ▲]

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See detailRegularization and Stabilization of Singular Fractional-Order Systems
Ndoye, Ibrahima UL; Zasadzinski, Michel; Darouach, Mohamed et al

in 4th IFAC Workshop Fractional Differentiation and its Applications, Badajoz, Spain, 2010 (2010)

In this paper, asymptotical stabilization problem via a predictive and memoryless static feedbacks of singular fractional-order systems is investigated. Sufficient linear matrix inequalities (LMI ... [more ▼]

In this paper, asymptotical stabilization problem via a predictive and memoryless static feedbacks of singular fractional-order systems is investigated. Sufficient linear matrix inequalities (LMI) conditions for regularization of singular fractional-order systems are given. Then, the predictive controller aims to regularizing the singular fractional-order systems while the memoryless state feedback is designed to stabilize the resulting regularized system. The result can be applicable to the asymptotical stabilization problem of a class of nonlinear singular fractional-order systems using a new generalization of Gronwall-Bellman lemma. [less ▲]

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See detailStabilisation des systèmes bilinéaires fractionnaires
Ndoye, Ibrahima UL; Zasadzinski, Michel; Nour-Eddine, Radhy et al

in Sixième Conférence Internationale Francophone d'Automatique, CIFA 2010, Nancy, France (2010)

Cet article traite de la stabilisation des systèmes bilinéaires fractionnaires par l'approche de la nouvelle généralisation du lemme de Gronwall-Bellman. L'utilisation de cette nouvelle approche permet de ... [more ▼]

Cet article traite de la stabilisation des systèmes bilinéaires fractionnaires par l'approche de la nouvelle généralisation du lemme de Gronwall-Bellman. L'utilisation de cette nouvelle approche permet de montrer sous certaines hypothèses adéquates, qu'on peut garantir une stabilisation asymptotique par retour d'état statique et par retour de sortie statique des systèmes bilinéaires fractionnaires. La méthodologie est illustrée par l'intermédiaire d'un exemple numérique. [less ▲]

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See detailStabilization of Singular Fractional-Order Systems : An LMI Approach
Ndoye, Ibrahima UL; Zasadzinski, Michel; Radhy, Nour-Eddine et al

in 18th IEEE Mediterranean Conference on Control & Automation, Morocco, June 23-25, 2010 (2010)

This paper presents the asymptotical stabilization problem of linear singular fractional-order systems. The results are obtained in terms of linear matrix inequalities, which are derived using the ... [more ▼]

This paper presents the asymptotical stabilization problem of linear singular fractional-order systems. The results are obtained in terms of linear matrix inequalities, which are derived using the decomposition on the matrices of the original system. An illustrative example is provided to illustrate the proposed [less ▲]

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See detailExponential Observer-Based Stabilization for a Class of Affine Nonlinear Systems
Ndoye, Ibrahima UL; Zasadzinski, Michel; Radhy, Nour-Eddine et al

in 14th International IEEE/IFAC Conference Methods and Models in Automation and Robotics, MMAR’09botics MMAR'09, Poland, 19 - 21 August 2009 (2009)

In this paper, we investigate the problem of stabilizing a class of nonlinear affine systems by using the generalization of Gronwall-Bellman lemma with two control laws: first a nonlinear state feedback ... [more ▼]

In this paper, we investigate the problem of stabilizing a class of nonlinear affine systems by using the generalization of Gronwall-Bellman lemma with two control laws: first a nonlinear state feedback and second a nonlinear observer-based control. The obtained closed-loop stability is exponential. [less ▲]

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See detailStabilization of a Class of Nonlinear Affine Fractional-Order Systems using Generalizations of Bellman-Gronwall Lemma
Ndoye, Ibrahima UL; Zasadzinski, Michel; Radhy, Nour-Eddine et al

in 17th IEEE Mediterranean Conference on Control & Automation MED'09, Thessaloniki, Greece, 2009 (2009)

This paper presents a result of stabilization of nonlinear affine fractional-order systems using generalizations of Gronwall-Bellman lemma. Two case are treated: the nonlinear and the linear state ... [more ▼]

This paper presents a result of stabilization of nonlinear affine fractional-order systems using generalizations of Gronwall-Bellman lemma. Two case are treated: the nonlinear and the linear state feedback stabilization. [less ▲]

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See detailObserver-Based Control for Fractional-Order Continuous-Time Systems
Ndoye, Ibrahima UL; Zasadzinski, Michel; Darouach, Mohamed et al

in 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, Chine, December 16-18, 2009 (2009)

In this paper, we study the asymptotic stabilization of fractional-order systems using an observer-based control law. The fractional-order systems under consideration are either linear or nonlinear and ... [more ▼]

In this paper, we study the asymptotic stabilization of fractional-order systems using an observer-based control law. The fractional-order systems under consideration are either linear or nonlinear and affine. A generalization of Gronwall-Bellman which is proved in the appendix is used to derive the closed-loop asymptotic stability. [less ▲]

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See detailStabilization of a Class of Nonlinear Affine Fractional-Order Systems
Ndoye, Ibrahima UL; Zasadzinski, Michel; Darouach, Mohamed et al

in 14th International IEEE/IFAC Conference Methods and Models in Automation and Robotics, MMAR’09, Poland, June 24-26, 2009 (2009)

This paper deals with the asymptotical stabilization of nonlinear affine fractional-order systems. Two static control laws are considered: state and output feedbacks. The asymptotic stability is proven ... [more ▼]

This paper deals with the asymptotical stabilization of nonlinear affine fractional-order systems. Two static control laws are considered: state and output feedbacks. The asymptotic stability is proven using a proposed generalization of the Gronwall-Bellman lemma. [less ▲]

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