Observer-Based Approach for Fractional-Order Chaotic Synchronization and Secure Communication

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 ▲]

Design of Unkown Input Fractional-Order Observers for Fractional-Order Systems

in International Journal of Applied Mathematics and 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 ▲]

H-infinity Static Output Feedback Control for a Fractional-Order Glucose-Insulin System

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 ▲]

Fractional-Order Observers Design for Fractional-Order Systems with Unknown Inputs

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 ▲]

An Unknown Input Fractional-Order Observer Design for Fractional-Order Glucose-Insulin System

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 ▲]

Regularization and Robust Stabilization of Singular Uncertain Fractional-Order Systems

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 ▲]

Robust Stabilization of Linear and Nonlinear Fractional-Order Systems with Nonlinear Uncertain Parameters

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 ▲]

Stabilization of Singular Fractional-Order Systems : An LMI Approach

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 ▲]

Robust Controller Design for Linear Fractional-Order Systems with Nonlinear Time-Varying Model Uncertainties

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

In this article, a robust linear controller design in time domain is presented for linear fractional-order systems with nonlinear model uncertainties. The Gronwall-Bellman lemma is employed to investigate ... [more ▼]

In this article, a robust linear controller design in time domain is presented for linear fractional-order systems with nonlinear model uncertainties. The Gronwall-Bellman lemma is employed to investigate the robust stability conditions which are based on the upper norm-bounds of the uncertainties. The parameters of a dynamic controller are selected to satisfy the requirements of robust stability under plant uncertainties. [less ▲]

Exponential Observer-Based Stabilization for a Class of Affine Nonlinear Systems

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 ▲]