New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous differenc...

In this paper, the problem of asymptotical stability of neutral systems with nonlinear perturbations is investigated. Based on a class of novel augment Lyapunov functionals which contain freeweighting matrices, some new delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs) by using new inequality analysis technique. Numerical examples are g...

In this paper, we mainly study the Lyapunov asymptotical stability of linear and interval linear fractional order neutral systems with time delay. By applying the characteristic equations of these two systems, some simple sufficient Lyapunov asymptotical stability conditions are deserved, which are quite different from other ones in literature. In addition, some numerical examples are provided ...

This paper investigates the global asymptotical stability problems for delayed neural networks. By introducing some triple integral terms in the constructing of the Lyapunov-Krasovskii functional, combined with the inequality analysis, a new asymptotical stability condition in terms of linear matrix inequalities are proposed, Finally, numerical example is given to demonstrate the effectiveness ...

The Lyapunov function method is the focus of this paper in proving marginal stability, asymptotical or globally asymptotical stability of discrete dynamic systems. We show that the slightly relaxed versions of the well known sucient conditions are also necessary. Ó 2000 Elsevier Science Inc. All rights reserved. AMS: 90A16

In this paper, we study the stability of the nonlinear hybrid system describing the concentrations of extracellular and intracellular substances in the process of bio-dissimilation of glycerol to 1,3-propanediol. We prove an asymptotical stability lemma in nonlinear impulsive hybrid systems and obtain the strict stability and uniformly asymptotical stability for the nonlinear hybrid system. The...

Global phase synchronization for a class of dynamical complex networks composed of multiinput multioutput pendulum-like systems with time-varying coupling delays is investigated. The problem of the global phase synchronization for the complex networks is equivalent to the problem of the asymptotical stability for the corresponding error dynamical networks. For reducing the conservation, no line...

The stability of a neural network model may often be destroyed by the parameter deviations during the implementation. However, few results (if any) for the asymptotical stability of such system with a certain degree of parameter deviations have been reported in the literature. In this paper, we present a simple delayed neural network model, in which each parameter deviates the reference point w...

In this work, we extend the mathematical model of leptospirosis disease by taking into account the exposed individuals, the related death rate and the transmission coefficients between susceptible human and infected vector. Initially, we present the local asymptotical stability of both the disease-free and endemic equilibrium. We use the Lyapunov function theory with some sufficient conditions....