In this paper, the concept of practical output feedback controller for Takagi-Sugeno fuzzy models... more In this paper, the concept of practical output feedback controller for Takagi-Sugeno fuzzy models is introduced. Some new sufficient conditions are obtained to ensure the exponential stability using state estimation of the fuzzy control systems in presence of perturbations. We show that all state trajectories of the closed-loop fuzzy system are bounded and approach a sufficiently small neighborhood of the origin. First we consider the stability with state feedback fuzzy controllers and a natural form of observers for the considered models is designed where some restrictions are imposed on the perturbations for their practical exponential convergence. We then show that the state feedback controller and the observer always yield a stabilizing output feedback controller provided that the stabilizing property of the control and the asymptotic convergence of the observer are guaranteed by the Lyapunov method using positive definite matrices. In this sense, it is shown that the separation principle holds, the challenges are discussed and some analysis oriented tools are provided. An example in dimensional two is given to show the effectiveness of the proposed fuzzy-observer-based control approach.
We present in this paper some retarded integral inequalities of Gronwall type. The obtained resul... more We present in this paper some retarded integral inequalities of Gronwall type. The obtained results can be used to discuss the behavior of integral equations.
In this paper, we treat the class of nonlinear uncertain dynamic systems that was considered in [... more In this paper, we treat the class of nonlinear uncertain dynamic systems that was considered in [1, 5, 9, 10]. We consider continuous-time dynamical systems whose nominal part is linear and whose uncertain part is norm-bounded. We study the problems of state observation and obtaining stabilizing controller for uncertain nonlinear systems, where the uncertainties are characterized by known bounds.
In this paper, we present a practical Mittag Leffler stability for fractional-order nonlinear sys... more In this paper, we present a practical Mittag Leffler stability for fractional-order nonlinear systems depending on a parameter. A sufficient condition on practical Mittag Leffler stability is given by using a Lyapunov function. In addition, we study the problem of stability and stabilization for some classes of fractional-order systems.
UDC 517.9 This paper deals with the problem of stability of nonlinear differential equations with... more UDC 517.9 This paper deals with the problem of stability of nonlinear differential equations with perturbations. Sufficient conditions for global uniform asymptotic stability in terms of Lyapunov-like functions and integral inequality are obtained. The asymptotic behavior is studied in the sense that the trajectories converge to a small ball centered at the origin. Furthermore, an illustrative example in the plane is given to verify the effectiveness of the theoretical results.
In this paper, we investigate the problem of stability of time-varying stochastic perturbed singu... more In this paper, we investigate the problem of stability of time-varying stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. Sufficient conditions on uniform exponential stability and practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems are obtained based upon Lyapunov techniques. Furthermore, we study the problem of stability and stabilization of some classes of stochastic singular systems. Finally, we provide numerical examples to validate the effectiveness of the main results of this paper.
In this paper, the feedback control for a class of bilinear control systems with a small paramete... more In this paper, the feedback control for a class of bilinear control systems with a small parameter is proposed to guarantee the existence of limit cycle. We use the perturbation method of seeking in approximate solution as a finite Taylor expansion of the exact solution. This perturbation method is to exploit the "smallness" of the perturbation parameter e to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for this class of nonlinear control systems.
ABSTRACT In this paper, practical stability with respect to a part of the variables of nonlinear ... more ABSTRACT In this paper, practical stability with respect to a part of the variables of nonlinear stochastic differential equations is studied. The analysis of the global practical uniform asymptotic stability, the global practical uniform pth moment exponential stability, as well as the global practical uniform exponential stability with respect to a part of the variables of SDEs are carried out by using the Lyapunov techniques. Some illustrative examples to show the usefulness of the stability with respect to a part of variables notion are also provided.
This paper presents an algebraic approach to the problem of nonlinear observer design. We show, t... more This paper presents an algebraic approach to the problem of nonlinear observer design. We show, that an observer which converges globally and asymptotically can be designed for a class of homogeneous systems of odd degree.
In this paper, we address the problem of output feedback stabilization for a class of uncertain d... more In this paper, we address the problem of output feedback stabilization for a class of uncertain dynamical systems. An asymptotically stabilizing controller is proposed under the assumption that the nominal system is absolutely stable.
ABSTRACT In this paper, the Barbalat-type lemmas for conformable fractional order integrals which... more ABSTRACT In this paper, the Barbalat-type lemmas for conformable fractional order integrals which can be used to conclude the convergence of a function to zero is discussed.
Dans cette these, on etudie quelques problemes de stabilisation par retour d'etat pour certai... more Dans cette these, on etudie quelques problemes de stabilisation par retour d'etat pour certains systemes non lineaires. On donne des conditions suffisantes pour stabiliser globalement des systemes non lineaires en cascade. On considere en particulier une classe de systemes partiellement lineaires pour lesquels un feedback presque regulier stabilisant est explicitement donne. Pour les systemes de la forme x = ax + bu + f(x,u) avec une sortie lineaire y = cx, on montre que, sous des hypotheses sur la partie non lineaire, on peut les stabiliser par retour d'etat estime par un observateur. On donne en particulier une generalisation d'un resultat de tsinias. Le dernier chapitre de la these consiste a etudier la stabilisabilite des systemes non lineaires dans le plan de la forme x = p(x) + ubx ou p est un champ de vecteurs polynomial homogene de degre impair. Des conditions necessaires et suffisantes pour stabiliser globalement sont donnees
In this paper we present some sufficient conditions for the robust stability and stabilization of... more In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain
2015 World Symposium on Mechatronics Engineering & Applied Physics (WSMEAP), 2015
ABSTRACT In this paper we deal with the stability analysis problem of a class of nonautonomous de... more ABSTRACT In this paper we deal with the stability analysis problem of a class of nonautonomous delayed nonlinear systems. Using a Lyapunov–Krasovskii functional, some stability conditions are formulated and the practical stability of the proposed system is proved. Finally, illustrative examples with simulation results are given to demonstrate the validity of the result
In this paper, the concept of practical output feedback controller for Takagi-Sugeno fuzzy models... more In this paper, the concept of practical output feedback controller for Takagi-Sugeno fuzzy models is introduced. Some new sufficient conditions are obtained to ensure the exponential stability using state estimation of the fuzzy control systems in presence of perturbations. We show that all state trajectories of the closed-loop fuzzy system are bounded and approach a sufficiently small neighborhood of the origin. First we consider the stability with state feedback fuzzy controllers and a natural form of observers for the considered models is designed where some restrictions are imposed on the perturbations for their practical exponential convergence. We then show that the state feedback controller and the observer always yield a stabilizing output feedback controller provided that the stabilizing property of the control and the asymptotic convergence of the observer are guaranteed by the Lyapunov method using positive definite matrices. In this sense, it is shown that the separation principle holds, the challenges are discussed and some analysis oriented tools are provided. An example in dimensional two is given to show the effectiveness of the proposed fuzzy-observer-based control approach.
We present in this paper some retarded integral inequalities of Gronwall type. The obtained resul... more We present in this paper some retarded integral inequalities of Gronwall type. The obtained results can be used to discuss the behavior of integral equations.
In this paper, we treat the class of nonlinear uncertain dynamic systems that was considered in [... more In this paper, we treat the class of nonlinear uncertain dynamic systems that was considered in [1, 5, 9, 10]. We consider continuous-time dynamical systems whose nominal part is linear and whose uncertain part is norm-bounded. We study the problems of state observation and obtaining stabilizing controller for uncertain nonlinear systems, where the uncertainties are characterized by known bounds.
In this paper, we present a practical Mittag Leffler stability for fractional-order nonlinear sys... more In this paper, we present a practical Mittag Leffler stability for fractional-order nonlinear systems depending on a parameter. A sufficient condition on practical Mittag Leffler stability is given by using a Lyapunov function. In addition, we study the problem of stability and stabilization for some classes of fractional-order systems.
UDC 517.9 This paper deals with the problem of stability of nonlinear differential equations with... more UDC 517.9 This paper deals with the problem of stability of nonlinear differential equations with perturbations. Sufficient conditions for global uniform asymptotic stability in terms of Lyapunov-like functions and integral inequality are obtained. The asymptotic behavior is studied in the sense that the trajectories converge to a small ball centered at the origin. Furthermore, an illustrative example in the plane is given to verify the effectiveness of the theoretical results.
In this paper, we investigate the problem of stability of time-varying stochastic perturbed singu... more In this paper, we investigate the problem of stability of time-varying stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. Sufficient conditions on uniform exponential stability and practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems are obtained based upon Lyapunov techniques. Furthermore, we study the problem of stability and stabilization of some classes of stochastic singular systems. Finally, we provide numerical examples to validate the effectiveness of the main results of this paper.
In this paper, the feedback control for a class of bilinear control systems with a small paramete... more In this paper, the feedback control for a class of bilinear control systems with a small parameter is proposed to guarantee the existence of limit cycle. We use the perturbation method of seeking in approximate solution as a finite Taylor expansion of the exact solution. This perturbation method is to exploit the "smallness" of the perturbation parameter e to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for this class of nonlinear control systems.
ABSTRACT In this paper, practical stability with respect to a part of the variables of nonlinear ... more ABSTRACT In this paper, practical stability with respect to a part of the variables of nonlinear stochastic differential equations is studied. The analysis of the global practical uniform asymptotic stability, the global practical uniform pth moment exponential stability, as well as the global practical uniform exponential stability with respect to a part of the variables of SDEs are carried out by using the Lyapunov techniques. Some illustrative examples to show the usefulness of the stability with respect to a part of variables notion are also provided.
This paper presents an algebraic approach to the problem of nonlinear observer design. We show, t... more This paper presents an algebraic approach to the problem of nonlinear observer design. We show, that an observer which converges globally and asymptotically can be designed for a class of homogeneous systems of odd degree.
In this paper, we address the problem of output feedback stabilization for a class of uncertain d... more In this paper, we address the problem of output feedback stabilization for a class of uncertain dynamical systems. An asymptotically stabilizing controller is proposed under the assumption that the nominal system is absolutely stable.
ABSTRACT In this paper, the Barbalat-type lemmas for conformable fractional order integrals which... more ABSTRACT In this paper, the Barbalat-type lemmas for conformable fractional order integrals which can be used to conclude the convergence of a function to zero is discussed.
Dans cette these, on etudie quelques problemes de stabilisation par retour d'etat pour certai... more Dans cette these, on etudie quelques problemes de stabilisation par retour d'etat pour certains systemes non lineaires. On donne des conditions suffisantes pour stabiliser globalement des systemes non lineaires en cascade. On considere en particulier une classe de systemes partiellement lineaires pour lesquels un feedback presque regulier stabilisant est explicitement donne. Pour les systemes de la forme x = ax + bu + f(x,u) avec une sortie lineaire y = cx, on montre que, sous des hypotheses sur la partie non lineaire, on peut les stabiliser par retour d'etat estime par un observateur. On donne en particulier une generalisation d'un resultat de tsinias. Le dernier chapitre de la these consiste a etudier la stabilisabilite des systemes non lineaires dans le plan de la forme x = p(x) + ubx ou p est un champ de vecteurs polynomial homogene de degre impair. Des conditions necessaires et suffisantes pour stabiliser globalement sont donnees
In this paper we present some sufficient conditions for the robust stability and stabilization of... more In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain
2015 World Symposium on Mechatronics Engineering & Applied Physics (WSMEAP), 2015
ABSTRACT In this paper we deal with the stability analysis problem of a class of nonautonomous de... more ABSTRACT In this paper we deal with the stability analysis problem of a class of nonautonomous delayed nonlinear systems. Using a Lyapunov–Krasovskii functional, some stability conditions are formulated and the practical stability of the proposed system is proved. Finally, illustrative examples with simulation results are given to demonstrate the validity of the result
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Papers by Mohamed Hammami