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In this paper, we present a converse Lyapunov theorem for the new notion of global generalized practical uniform h-stability of nonlinear systems of differential equations. We derive some sufficient conditions which guarantee the global generalized practical uniform h-stability of time-varying perturbed systems. In addition, these results are used to study the practical h-stability of models of infectious diseases and vaccination. [ABSTRACT FROM AUTHOR]

We develop tools for the investigation of input-to-state practical stability (ISpS) and integral input-to-state practical stability (iISpS) of non-autonomous infinite-dimensional systems in Banach spaces. Sufficient conditions of ISpS and iISpS are given based on indefinite Lyapunov functions. The practical stability analysis is accomplished with the help of scalar practical stable functions. Then, a construction of ISpS Lyapunov function for a class of non-autonomous evolutions equations is provided in Hilbert spaces. We propose the ISpS Lyapunov methodology to make it suitable for the analysis of ISpS w.r.t. inputs from $ L_p $ L p -spaces. Furthermore, we illustrate the theory with an example of a semi-linear reaction-diffusion equation. [ABSTRACT FROM AUTHOR]

The asymptotic behavior of solutions of fuzzy control systems is a component of the study of fuzzy control theory. The study of stability for T-S (Takagi-Sugeno) fuzzy systems, which process qualitative data through linguistic expressions, is the subject of this paper. Asymptotic stability is conservative in many real-world applications due to measurement noise and other disruptions. The ultimate limit, which indicates that the mistakes stay in a specific area close to the origin after a long enough amount of time, is a crucial characteristic that is frequently defined for such systems. We are interested with the problem of the state feedback controller for T-S fuzzy models with uncertainties where the global exponential ultimate boundedness of solutions is studied for certain fuzzy control systems. We use common quadratic Lyapunov function and parallel distributed compensation controller techniques to study the asymptotic behavior of the solutions of fuzzy control system in presence of perturbations. An example demonstrating the validity of the main result is discussed. [ABSTRACT FROM AUTHOR]

In this article, we are concerned with the input‐to‐state practical stability (ISpS) of nonautonomous nonlinear infinite‐dimensional systems. Sufficient conditions of ISpS are provided based on Lyapunov functions and a nonlinear inequality. We characterize ISpS in terms of uniform practical asymptotic gain property. We show that for a class of admissible inputs the existence of an ISpS‐Lyapunov function implies the ISpS of a system in Banach spaces. These results are used to study the input‐to‐state practical stability of a certain class of nonautonomous semilinear evolution equations. Furthermore, we provide a small‐gain theorem for nonautonomous nonlinear interconnected systems. An example is used to illustrate the application of the developed method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of global practical exponential stability for Takagi-Sugeno fuzzy systems in presence of perturbations. The proposed approach for stability analysis is based on the determination of the bounds of perturbations that characterize the asymptotic convergence of the solutions to a small ball centered at the origin. The goal is to study systems whose desired behavior is asymptotic stability about the origin of the state space or a close approximation to this. All state trajectories are bounded and approach a sufficiently small neighborhood of the origin under some perurbations. The effectiveness of the presented criterion is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

The approach of Lyapunov functions is one of the most efficient ones for the investigation of the stability of stochastic systems, in particular, of singular stochastic systems. The main objective of the paper is the analysis of the stability of stochastic perturbed singular systems by using Lyapunov techniques under the assumption that the initial conditions are consistent. The uniform exponential stability in mean square and the practical uniform exponential stability in mean square of solutions of stochastic perturbed singular systems based on Lyapunov techniques are investigated. Moreover, we study the problem of stability and stabilization of some classes of stochastic singular systems. Finally, an illustrative example is given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this article, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non‐necessarily small perturbations. We show that, under some estimates on the perturbation term, the equilibrium point remains (globally) uniformly exponentially stable. The obtained stability results can easily be applied in practice since they are based on the Gronwall–Bellman inequalities rather than the classical Lyapunov methods that require the knowledge of a Lyapunov function. Several numerical examples, as well as an application to control and mechanical systems, are given in illustration. [ABSTRACT FROM AUTHOR]

The Lyapunov's second method is one of the most famous techniques for studying the stability properties of dynamic systems. This technique uses an auxiliary function, called Lyapunov function, which checks the stability properties of a specific system without the need to generate system solutions. An important question is about the reversibility or converse of Lyapunov's second method; i. e., given a specific stability property does there exist an appropriate Lya-punov function? The main result of this paper is a converse Lyapunov Theorem for practical asymptotic stable impulsive systems. Applying our converse Theorem, several criteria on prac-tical asymptotic stability of the solution of perturbed impulsive systems and cascade impulsive systems are established. Finally, some examples are given to show the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global uniform practical exponential stability for a class of uncertain Takagi-Sugeno fuzzy systems. The uncertainties are supposed uniformly to be bounded by some known integrable functions to obtain an exponential convergence toward a neighborhood of the origin. Therefore, we use common quadratic Lyapunov function (CQLF) and parallel distributed compensation (PDC) controller techniques to show the global uniform practical exponential stability of the closed-loop system. Numeric simulations are given to validate the proposed approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 (SDEs) 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 solutions of SDEs based on Lyapunov techniques are investigated. Furthermore, an example is given to illustrate the applicability of the main result. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of stability analysis of systems with delayed time-varying perturbations. Some sufficient conditions for a class of linear time-varying systems with nonlinear delayed perturbations are derived by using an improved Lyapunov-Krasovskii functional. The uniform global asymptotic stability of the solutions is obtained in terms of convergence toward a neighborhood of the origin. [ABSTRACT FROM AUTHOR]

The objective of this work is twofold. In the first part, we present sufficient conditions for global uniform asymptotic stability and/or practical stability in terms of Lyapunov-like functions for nonlinear time varying systems. Furthermore, an illustrative numerical example is presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, global and local uniform asymptotic stability of perturbed dynamical systems is studied by using Lyapunov techniques. The restriction about the perturbed term is that the perturbation is bounded by an integrable function under the assumption that the nominal system is globally uniformly asymptotically stable. We use a new Lyapunov function to obtain a global uniform asymptotical stability of some perturbed systems. [Copyright &y& Elsevier]