Ibrahima N'Doye

Robust stabilization of uncertain descriptor fractional-order systems

This paper presents sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional order @a satisfying 0<@a<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 @a belonging to 0<@a<2 is derived. Two numerical examples are given to demonstrate the applicability of the proposed approach.

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

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.

Design of unknown input fractional-order observers for fractional-order systems

Abstract This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 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 α belongs to 1≤α<2 and 0<α≤1, respectively. A stability analysis of the fractional-order error system is made 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.

Observer-based control for fractional-order continuous-time systems

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.

Stabilization of singular fractional-order systems: An LMI approach

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 results.

An unknown input fractional-order observer design for fractional-order glucose-insulin system

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 α belonging to 0 <; α <; 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.

Stabilization of a class of nonlinear affine fractional-order systems using generalizations of Bellman-Gronwall lemma

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

Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 <; α <; 1. A numerical example is given to demonstrate the validity of the proposed approach.

Robust stabilization of linear and nonlinear fractional-order systems with nonlinear uncertain parameters

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.

Observers design for singular fractional-order systems

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.