On se propose d’étudier la stabilité d’une poutre flexible homogène, encastrée à une extrémité. À l’autre extrémité est attachée une masse ponctuelle où on applique un moment proportionnel à la vitesse de déplacement angulaire. On montre par une analyse spectrale que le taux optimal de décroissance de l’énergie est déterminé par l’abscisse spectrale du générateur infinitésimal du semi-groupe associé au problème.

We study the stability of a flexible beam clamped at one end. A mass is attached at the other end, where a control moment is applied. The boundary control is proportional to the angular velocity at the end. By spectral analysis, we prove that the optimal decay rate of the energy is given by the spectrum of the generator of the semigroup associated to the system.

Dans ce travail, nous étudions la propriété de base de Riesz et la stabilisation exponentielle pour une équation des poutres d’Euler-Bernoulli à coefficients variables sous un contrôle frontière linéaire dépendant de la position (resp. l’angle de rotation), de la vitesse et de la vitesse de rotation dans le contrôle force (resp. moment). Nous montrons qu’il existe une suite de fonctions propres généralisées qui forme une base de Riesz de l’espace d’énergie considéré, et qu’il y a stabilité exponentielle...

The problem of boundary stabilization for the isotropic linear elastodynamic system and the wave equation with Ventcel's conditions are considered (see [12]). The boundary observability and the exact controllability were etablished in [11]. We prove here the enegy decay to zero for the elastodynamic system with stationary Ventcel's conditions by introducing a nonlinear boundary feedback. We also give a boundary feedback leading to arbitrarily large energy decay rates for the elastodynamic system...

On considère l’équation des ondes sur un rectangle avec un feedback de type Dirichlet. On se place dans le cas où la condition de contrôle géométrique n’est pas satisfaite (BLR Condition), ce qui implique qu’on n’a pas stabilité exponentielle dans l’espace d’énérgie. On prouve qu’on peut trouver un sous espace de l’espace d’énergie tel qu’on a stabilité exponentielle. De plus, on montre un résultat de décroissance polynomiale pour toute donnée initiale régulière.

On s'intéresse dans cet article, a la stabilisation de l'équation des ondes dans un domaine extérieur avec condition de Dirichlet...

Dans ce travail, nous étudions une équation des poutres d’Euler-Bernoulli, on contrôle par combinaison linéaire de vitesse et vitesse de rotation appliquées à l’une des extrémités du système. Tout d’abord nous montrons que le problème est bien posé et qu’il y a stabilité uniforme sous certaines conditions portant sur les coefficients de feedback. Puis nous estimons le taux optimal de décroissance de l’énergie du système par la méthode de Shkalikov.

A controller architecture for nonlinear systems described by Gaussian RBF neural networks is proposed. The controller is a stabilising solution to a class of nonlinear optimal state tracking problems and consists of a combination of a state feedback stabilising regulator and a feedforward neuro-controller. The state feedback stabilising regulator is computed on-line by transforming the tracking problem into a more manageable regulation one, which is solved within the framework of a nonlinear predictive...

Soient $X$ et $Y$ deux champs de vecteurs lisses sur ${ℝ}^2$ globalement asymptotiquement stables à l’origine. Nous donnons des conditions nécessaires et des conditions suffisantes sur la topologie de l’ensemble des points où $X$ et $Y$ sont parallèles pour pouvoir assurer la stabilité asymptotique globale du système contrôlé non linéaire non autonome$$\dot{q}\left(t\right)=u\left(t\right)X\left(q\left(t\right)\right)+(1-u\left(t\right))Y\left(q\left(t\right)\right)$$où le contrôle $u$ est une fonction mesurable arbitraire de $[0,+\infty [$ dans $\{0,1\}$. Les conditions données ne nécessitent aucune intégration ou construction d’une fonction de Lyapunov...

This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T-S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain...

In this paper we consider a linear system subject to norm bounded, bounded rate time-varying uncertainties. Necessary and sufficient conditions for quadratic stability and stabilizability of such class of uncertain systems are well known in the literature. Quadratic stability guarantees exponential stability in presence of arbitrary time-varying uncertainties; therefore it becomes a conservative approach when, as it is the case considered in this paper, the uncertainties are slowly-varying in time....

This paper is concerned with the problem of the exponential stability in mean square moment for neutral stochastic systems with mixed delays, which are composed of the retarded one and the neutral one, respectively. Based on an integral inequality, a delay-dependent stability criterion for such systems is obtained in terms of linear matrix inequality (LMI) to ensure a large upper bounds of the neutral delay and the retarded delay by dividing the neutral delay interval into multiple segments. A new...

This paper considers a three-dimensional energy demand-supply system which typically demonstrates the relationship between the amount of energy supply and that of energy demand for the two regions in China. A delayed feedback controller is proposed to stabilize the system which was originally unstable even under some other controllers. The stability properties of the equilibrium points are subsequently analyzed and it is found that the Hopf bifurcation appears under some conditions. By using the...

In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized...

This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous...