General Decay Pathwise Stability of Neutral Stochastic Differential Equations with Unbounded Delay

Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence^and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.

Robust Exponential Stability of Switched Interval Interconnected Systems with Unbounded Delay

In this paper, a class of switched interval interconnected systems with unbounded delay were investigated. On the assumption that the interconnected functions of the systems satisfied the global Lipschitz condition, by using vector Lyapunov methods and M-matrix theory, the integrodifferential inequalities with unbounded delay were constructed. By the stability analysis of the integrodifferential inequalities, the sufficient conditions to ensure the robust exponential stability of the interval interconnected systems were obtained. By using average dwell time approach, conditions for guaranteeing the robust exponential stability of the switched delay interval interconnected systems were derived.Finally, two numerical examples were given to illustrate the correction and effectiveness of the proposed theory.

OSCILLATION OF SOLUTIONS FOR A CLASS OF UNBOUNDED DELAY DIFFERENTIAL EQUATIONS

In this paper we present infinite-integral conditions for the oscillation of a class of unbounded delay differential equations.

On the Existence,Uniqueness and Stability of Periodic Solutions of Large Scale Systems with Unbounded Delay

In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.

On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays

Recent years have witnessed the surge of asynchronous parallel(asyncparallel)iterative algorithms due to problems involving very large-scale data and a large number of decision variables.Because of asynchrony,the iterates are computed with outdated information,and the age of the outdated information,which we call delay,is the number of times it has been updated since its creation.Almost all recent works prove convergence under the assumption of a finite maximum delay and set their stepsize parameters accordingly.However,the maximum delay is practically unknown.This paper presents convergence analysis of an async-parallel method from a probabilistic viewpoint,and it allows for large unbounded delays.An explicit formula of stepsize that guarantees convergence is given depending on delays’statistics.With p+1 identical processors,we empirically measured that delays closely follow the Poisson distribution with parameter p,matching our theoretical model,and thus,the stepsize can be set accordingly.Simulations on both convex and nonconvex optimization problems demonstrate the validness of our analysis and also show that the existing maximum-delay-induced stepsize is too conservative,often slows down the convergence of the algorithm.

ASYMPTOTIC STABILITY OF SINGULAR NONLINEAR DIFFERENTIAL SYSTEMS WITH UNBOUNDED DELAYS

In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.

STABILITY THEOREM FOR A CLASS OF PERTURBED NONAUTONOMOUS NEUTRAL DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this paper, we consider a one-dimensional nonautonomous neutral differential equation. We obtain sufficient conditions under which the zero solution to this equation with unbounded delay and perturbation is uniformly asymptotically stable.

GLOBAL ATTRACTIVITY OF A LOGISTIC MODEL WITH UNBOUNDED DELAY

In this paper, we consider the following Logistic model where {rn}n=0 is a sequence of nonnegative real number, {kn} is a sequence of nonnegative integers satisfying lim (n-kn)= , lim sup kn=∞ , and K is a positive constant. We obtain a new sufficient condition for the positive equilibrium of Eq.() to be globally attractive, which improves some recent known results established in [3-4].

ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING

The problem of robust exponential stability for a class of switched nonlineardynamical systems with uncertainties and unbounded delay is addressed. On the assump-tion that the interconnected functions of the studied systems satisfy the Lipschitz condition,by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions toensure the robust exponential stability of the switched interconnected systems under arbi-trary switching are obtained. The proposed method, which neither require the individualsubsystems to share a Common Lyapunov Function （CLF）, nor need to involve the values ofindividual Lyapunov functions at each switching time, provide a new way of thinking to studythe stability of arbitrary switching. In addition, the proposed criteria are explicit, and it isconvenient for practical applications. Finally, two numerical examples are given to illustratethe correctness and effectiveness of the proposed theories.

Uniform Boundedness for Neutral Equations with Unbouned Delay

We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.

Global exponential p-norm stability of BAM neural networks with unbounded time-varying delays:A method based on the representation of solutions

This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forward to deduce a global exponential p-norm stability criterion.This method does not need to set up any Lyapunov-Krasovskii functionals(LKF),which can greatly reduce a large amount of computations and is simpler than the existing methods.In the end,representative numerical examples are given to llustrate the availability of the method.

ON EXPONENTIAL STABILITY OF LARGE SCALE SYSTEMS WITH UNBOUNDED DELAY

In this paper, we first give a sufficient and necessary condition to guarantee the exponential stability of a special system with unbounded delay, then by using the delay-differential comparison theorem, obtain some simple criteria for the exponential stability of large scale systems with unbounded delay.

CONVERGENCE OF SOLUTIONS FOR A CLASS OF DIFFERENCE EQUATIONS WITH VARIABLE DELAY

In this paper, we study the convergence of solutions for a class of difference equations with variable delay and give some results about the solutions of the equations converge to a constant. Our results generalize the conclusions obtained in .

POSITIVE SOLUTIONS TO TWO TYPES OF NEUTRAL DIFFERENTIAL EQUATIONS WITH DISTRIBUTED DELAY

In this paper, we study two types of neutral functional differential equations with finite or unbounded distributed deviating arguments. By Banach contraction princi-ple, we obtain some sufficient conditions for the existence of positive solutions to such equations.

OSCILLATION CRITERIA FOR A CLASS OF FIRST-ORDER NEUTRAL PANTOGRAPH DIFFERENTIAL EQUATIONS OF EULER TYPE

In this paper, we further investigate a class of first order neutral Pantograph differential equations of Euler type by Guan and Shen . Some infinite-integral conditions for the oscillation of all solutions are established.

BOUNDEDNESS IN p-NFDES

This paper considers a class of p-NFDEs. By Liapunov functionals, we establish two boundedness criteria, which improve some boundedness conditions for FDEs in the literature. Some examples are also worked out to demonstrate the advantages of our results.