On the practical global uniform asymptotic stability of stochastic differential equations

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of stochastic differential equations by using Lyapunov functions when the origin is not necessarily an equilibrium point. The global uniform boundedness and the global practical uniform exponential stability of so- lutions of stochastic differential equations based on Lyapunov techniques are investigated. Furthermore, an example is given to illustrate the applicability of the main result.Comment: To appear in Stochastic

Growth conditions for the stability of a class of time-varying perturbed singular systems

summary:In this paper, we investigate the problem of stability of linear time-varying singular systems, which are transferable into a standard canonical form. Sufficient conditions on exponential stability and practical exponential stability of solutions of linear perturbed singular systems are obtained based on generalized Gronwall inequalities and Lyapunov techniques. Moreover, we study the problem of stability and stabilization for some classes of singular systems. Finally, we present a numerical example to validate the effectiveness of the abstract results of this paper

La sécurité des futures architectures convergentes pour des services personnalisés : aspect architectural et protocolaire

The emergence and evolution of Next Generation Networks (NGN) have raised several challenges mainly in terms of heterogeneity, mobility and security. In fact, the user is able, in such environment, to have access to many networks, via multiple devices, with a vast choice of services offered by different providers. Furthermore, end-users claim to be constantly connected anywhere, anytime and anyhow. Besides, they want to have a secure access to their services through a dynamic, seamless and continuous session according to their preferences and the desired QoS. In this context, security represents an important concern. In fact, this user-centric session should obviously be secured. However, many challenges arise. In such environment, system boundaries, which were well delimited, become increasingly open. Indeed, there are multiple services which are unknown in advance and multiple communications between services and with users. Besides, heterogeneity of involved resources (terminals, networks and services) in the user session increases the complexity of security tasks. In addition, the different types of mobility (user, terminal, network and service mobility) affect the user-centric session that should be unique, secure and seamless and ensure continuity of services.L’émergence et l’évolution des réseaux de nouvelles génération (NGN) a soulevé plusieurs défis surtout en termes d’hétérogénéité, de mobilité et de sécurité. En effet, l’utilisateur est capable, dans un tel environnement, d’avoir accès à plusieurs réseaux, à travers différents terminaux, avec un choix vaste de services fournis par différents fournisseurs. De plus, les utilisateurs finaux demandent à être constamment connectés n’importe où, n’importe quand et n’importe comment. Ils désirent également avoir un accès sécurisé à leurs services à travers une session dynamique, seamless et continue selon leurs préférences et la QoS demandée. Dans ce contexte, la sécurité représente une composante majeure. Face à cette session user-centric sécurisée, plusieurs défis se posent. L’environnement est de plus en plus ouvert, de multiples services ne sont pas connus d’avance et nous avons une diversité de communications entre les services et les utilisateurs. L’hétérogénéité des ressources (terminaux, réseaux et services) impliquées dans la session de l’utilisateur accentue la complexité des tâches de sécurité. Les différentes déclinaisons de mobilité (mobilité de l’utilisateur, mobilité du terminal, mobilité du réseau et mobilité du service) modifient la session user-centric que l’on veut unique, sécurisée et seamless avec la délivrance d’un service continu

Lyapunov functionals and practical stability for stochastic differential delay equations with general decay rate

This paper stands for the almost sure practical stability of nonlinear stochastic differential delay equations (SDDEs) with a general decay rate. We establish some sufficient conditions based upon the construction of appropriate Lyapunov functionals. Furthermore, we provide some numerical examples to validate the effectiveness of the abstract results of this paper

Practical exponential stability in mean square of stochastic partial differential equations

The main aim of this paper is to establish some criteria for the mean square and almost sure practical exponential stability of a nonlinear monotone stochastic partial differential equations

Practical asymptotic stability of nonlinear stochastic evolution equations

In this paper we establish some su cient conditions ensuring almost sure practical asymptotic stability with a non-exponential decay rate for solutions to stochastic evolution equations based on Lyapunov techniques

Practical stability of stochastic delay evolution equations

In this paper we investigate the almost sure practical stability for a class of stochastic functional evolution equations. We establish some sufficient conditions based on the construction of appropriate Lyapunov functional. The abstract results are then applied to some illustrative examples.Fondo Europeo de Desarrollo Regional (FEDER)Ministerio de Economía y Competitividad (España)Junta de Andalucí

Practical exponential stability of impulsive stochastic functional differential equations

This paper is devoted to the investigation of the practical exponential stability of impulsive stochastic functional differential equations. The main tool used to prove the results is the Lyapunov-Razumikhin method which has proven very useful in dealing with stability problems for differential systems when the delays involved in the equations are not differentiable but only continuous. An illustrative example is also analyzed to show the applicability and interest of the main results.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadJunta de Andalucí