一类非线性中立型系统的渐近稳定性

基于李雅普诺夫泛函方法,本文讨论了一类非线性中立型系统渐近稳定性的充分条件,推广了中立型系统稳定性结果。最后,通过实例及其仿真数值模拟验证了上述理论结果。     

New results for global stability of a class of neutral-type neural systems with time delays

This paper studies the global convergence properties of a class of neutral-type neural networks with discrete time delays. This class of neutral systems includes Cohen–Grossberg neural networks, Hopfield neural networks and cellular neural networks. Based on the Lyapunov stability theorems, some delay independent sufficient conditions for the global asymptotic stability of the equilibrium point for this class of neutral-type systems are derived. It is shown that the results presented in this paper for neutral-type delayed neural networks are the generalization of a recently reported stability result. A numerical example is also given to demonstrate the applicability of our proposed stability criteria.     

On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations

The issue of robustly exponential stability for uncertain neutral-type systems is considered in this paper. The uncertainties are nonlinear and the delays are time-varying. In terms of a linear matrix inequality (LMI), the new sufficient stability condition with delay dependence is presented. The model transformation and bounding techniques for cross terms are avoided based on an integral inequality. Two illustrative examples are proposed to show the effectiveness of our method.     

The stability of distributed neutral delay differential systems with Markovian switching

This paper is concerned with the stability analysis of neutral-type stochastic distributed delay differential systems described by Markovian switching. This system has some special kind of neutral behaviour with uncertain distributed time delays occurring in the state variables. Based on the Lyapunov function, novel methodologies for analyzing stability criteria, and the design of an uncertain distributed delay model are presented. The proposed method is an alternative way to study the robustness and stability of uncertain distributed delays with neutral systems. In order to demonstrate the applicability of the results, the investigation considers two specific examples.     

Improved results on robust exponential stability criteria for neutral-type delayed neural networks

In this paper, we investigate the problem of robust global exponential stability analysis for a class of neutral-type neural networks. The interval time-varying delays allow for both slow and fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. Improved global exponential stability condition is derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed nominal and robust stability criteria is delay-dependent and characterized by linear-matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.     

Stability analysis of fractional order neutral-type systems considering time varying delays,nonlinear perturbations,and input saturation

This article investigates the robust stability of fractional order neutral-type systems involving nonlinear perturbations and time varying delays in the presence of input saturation. Design criteria, expressed in terms of linear matrix inequalities, are derived with the aid of the Lyapunov Krasovskii functional for the state feedback controller. Based on the cone complementarity linearization method, an optimization problem is also formulated for finding the controller gains subject to maximizing the domain of attraction. The main results are confirmed by numerical simulations.     

On the approximation of nonlinear conflict-controlled systems of neutral type

We consider approximations of systems of nonlinear neutral-type equations in Hale’s form by systems of high-order ordinary differential equations. A procedure is given for the mutual feedback tracking between the motion of the original neutral-type conflict-controlled system and the motion of the approximating system of ordinary differential equations. The proposed mutual tracking procedure makes it possible to use approximating systems of ordinary differential equations as finite-dimensional modeling guides for neutral-type systems.     

Stability of Delayed Markovian Switching Stochastic Neutral-type Reaction-diffusion Neural Networks

This paper is concerned about exponential stability in mean square of Markovian switching delayed reaction-diffusion neutral-type stochastic neural networks (RNSNNs). By Lyapunov function method, several novel stability criteria on exponential mean square stability of Markovian switching RNSNNs with time-varying delays are obtained. In the end, two examples are given to verify the feasibility of our findings.     

Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays

In this paper, the global exponential stability for neutral-type impulsive neural networks with discrete and distributed delays is established by utilizing the Lyapunov–Krasovskii functional combining with the linear matrix inequality(LMI) approach.     

A semi-free weighting matrices approach for neutral-type delayed neural networks

In this paper, a new approach is proposed for stability issues of neutral-type neural networks (DNNs) with constant delay. First, the semi-free weighting matrices are proposed and used instead of the known free weighting matrices to express the relationship between the terms in the Leibniz–Newton formula to simplify the system synthesis and to obtain less computation demand. Second, global exponential stability conditions which are less conservative and restrictive than the known results are derived. At the same time, based on the above approach, fewer variable matrices are introduced in the construction of the Lyapunov functional and augmented Lyapunov functional. Two examples are given to show their effectiveness and advantages over others.     

Global attracting sets for neutral-type BAM neural networks with time-varying and infinite distributed delays

In this paper, the asymptotic property of a class of neutral-type BAM neural networks with time-varying and infinite distributed delays is discussed. By developing a new integral inequality and applying the properties of nonnegative matrix, some sufficient conditions for the Lagrange stability and the existence of the global attracting set of the considering model are obtained. Meanwhile, the estimation of the global attractive set is also given out. The results derived here generalize and improve the earlier publications. Finally, two numerical examples are given and analyzed to demonstrate our results.     

Global exponential stability results for neutral-type impulsive neural networks

In this paper, by utilizing the Lyapunov–Krasovkii functional and combining with the linear matrix inequality (LMI) approach, we analyze the global exponential stability of neutral-type impulsive neural networks. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

Stochastic global exponential stability for neutral-type impulsive neural networks with mixed time-delays and Markovian jumping parameters

This paper investigates the problem of the global exponential stability for neutral-type impulsive neural networks with mixed delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays and the jumping parameters are generated from a continuous time discrete state homogenous Markov process. Based on the Lyapunov functional, a sufficient criterion is derived in terms of linear matrix equality (LMI).     

一类五次系统赤道环的稳定性与极限环分枝

本文解决了一类五次系统赤道环的稳定性与极限环分枝问题，所得的结论与二次系统的若干结论形 成有趣的对比．     

Minimax solutions of Hamilton–Jacobi functional equations for neutral-type systems

A functional Hamilton–Jacobi equation with covariant derivatives which corresponds to neutral-type dynamical systems is obtained. The definition of a minimax solution of this equation is given. Conditions under which such a solution exists and is unique and well defined are found.     

STABILITY OF SOLUTION OF TIME-VARYING SINGULAR SYSTEMS WITH DELAY

1IntroductionInmanydifferentareas)ithasbeenfoundthatmanyproblemsaremodeledbysingularsystems,suchasoptimalcontrolproblemsandconstrainedcontrolproblems,electricalcircuits,somepopulationgrowthmodelsandsingularper-turbations.Sincedelayoftenoccursintheseproble…     

连续非自治系统的有限时间稳定性及其充分条件

本文研究了连续非自治系统的有限时间稳定性问题. 从一维连续非自治系统的有限时间稳定性分析入手, 本文通过使用比较原理, 获得了一些判定一般n维连续非自治系统的有限时间稳定性的充分条件,这些条件改善了已有的连续非自治系统有限时间稳定性的判定条件.     

大范围市场系统的稳定性分析

本文利用 L iapunov泛函的加权研究具时间滞后效应的大范围市场系统的稳定性 ,得到系统的均衡价格为一致渐近稳定的充分条件 ,它们推广或改进了文献 [1,4 ,5 ]的相应结果     

基于一类积分不等式上的中立型时滞微分方程的稳定性

利用一类积分不等式以及参数变易法,Jensen不等式,给出了更为一般的中立型时滞微分系统的Lyapunov稳定性的判别准则,推广和改进了一些文献中有关中立型微分方程的Lyapunov稳定性的结论.