具变时滞的非线性退化微分系统的渐近稳定性判据

In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigated. The asymptotic stability criteria for singular differential nonlinear systems with multiple time-varying delays are derived based on V-functional method and some analytical techniques, which are described as matrix equations or matrix inequalities. The results obtained are computationally flexible and efficient.     

变时滞的退化滞后型微分系统的稳定性

主要研究了具有变时滞的退化时滞微分系统的稳定性.利用退化时滞微分系统的变易公式和Gronwall-Bellman积分不等式给出了该系统的指数估计以及稳定和指数渐近稳定的充分条件.     

线性Volterra系统V泛函的构造及其应用

Ｖ泛函的构造是讨论Ｖｏｌｔｅｒｒａ积分微分系统稳定性的关键．近十年来，不少作者在Ｌｉａｐｕｎｏｖ泛函构造方面作了不少努力，但对一般的线性Ｖｏｌｔｅｒｒａ系统，还是没有构造Ｌｉｓｐｕｎｏｖ泛函通用而有效的方法．本文通过具体求解一个线性偏微分方程的方法来确定Ｖ泛函，得到了更广泛的Ｌｉａｐｕｎｏｖ泛函以及变号Ｖ泛函．同时，利用这些Ｖ泛函对线性Ｖｏｌｔｅｒｒａ系统的实用稳定性与Ｌｉｓｐｕｎｏｖ稳定性作了讨论．     

变时滞的退化中立型微分系统的稳定性

研究了具有变时滞的退化中立型微分系统的稳定性．利用退化时滞微分系统的变易公式和Gronwall-Bellman积分不等式给出了该系统的指数估计以及稳定和指数渐近稳定的充分条件．     

退化中立型微分系统的常数变易公式和通解

本文讨论退化中立型微分系统，将其分成三组系统，定义两种与其相应的基础解，并分别将其通解求出。从而给出退化中立型微分系统的通解以及常数变易公式，最终得出通解的明确表示，完全推广了常微分方程和时滞微分方程的基本理论。     

一类退化时滞微分系统解的稳定性

讨论了指标为1的退化时滞微分系统解的稳定性,并给出一个具体的V-泛函和相应的定理.     

一类具时滞的广义区间系统的稳定性分析

讨论了一类具时滞的广义区间系统的鲁棒稳定性.利用一般的自治退化时滞微分系统的稳定性的V 泛函判别定理给出相应区间系统的V 泛函和稳定性的判据.     

The Algebraic Criteria for the All-delay Stabilityof Two-dim ensional Degenerate Differential System swith Delay

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＡｓｔｈｅｄｅｅｐｌｙｄｅｖｅｌｏｐｍｅｎｔｏｆｔｈｅｓｔｕｄｙａｎｄａｐｐｌｉｃａｔｉｏｎｆｏｒｍａｎｙｐｒａｃｔｉｃａｌｓｙｓｔｅｍｓ，ｓｕｃｈａｓｅｃｏｎｏｍｉｃｍａｎａｇｅｍｅｎｔｓｙｓｔｅｍｓ，ｅｎｇｉｎｅｅｒｉｎｇｓｙｓｔｅｍｓ，ｐｏｗｅｒｓｙｓｔｅｍｓａｎｄｓｏｏｎ，ｐｅｏｐｌｅｄｅｖｏｔｅｍｕｃｈａｎｄｍｕｃｈａｔｔｅｎｔｉｏｎｔｏｔｈｅｐｈｅｎｏｍｅｎａｏｆｄｅｌａｙｓ［１］［２］．Ａｔｔｈｅｓａｍｅｔｉｍｅ，ｐｅｏｐｌｅｆｏｕｎｄｔｈａｔｔｈｅ…     

Stability in distribution of neutral stochastic functional differential equations with Markovian switching

Stability in distribution of stochastic differential equations with Markovian switching and stochastic differential delay equations with Markovian switching have been studied by several authors and this kind of stability is an important property for stochastic systems. There are several papers which study this stability for stochastic differential equations with Markovian switching and stochastic differential delay equations with Markovian switching technically. In our paper, we are concerned with the general neutral stochastic functional differential equations with Markovian switching and we derive the sufficient conditions for stability in distribution. At the end of our paper, one example is established to illustrate the theory of our work.     

一类具独立子系统的退化时滞控制系统的能控性

讨论退化时滞微分控制系统的能控性问题.首先将退化时滞微分控制系统化为标准形式,除去关联项,得到具独立子系统的退化时滞微分控制系统.然后就一般的退化时滞微分控制系统,得到其能控的充要条件为其可达集等于全空间.对于具独立子系统的广义时滞控制系统,给出其能控的充要条件为每个子系统的可达集等于其相应的子空间,并给出其能控的代数判据,最后举例说明主要结果的应用.     

Uniform asymptotic stability and global stability of impulsive infinite delay differential equations

This paper deals with the stability of a class of impulsive infinite delay differential equations. By using the Razumikhin technique and Lyapunov functions, we obtain a new criterion on the uniform asymptotic stability and global stability for such differential equations. The result is less restrictive and conservative than that given in some earlier references. Also, our result shows that impulses can make unstable systems stable. An example is given to illustrate the feasibility and advantage of the result.     

Numerical detection of instability regions for delay models with delay-dependent parameters

In this paper we are interested in gaining local stability insights about the interior equilibria of delay models arising in biomathematics. The models share the property that the corresponding characteristic equations involve delay-dependent coefficients. The presence of such dependence requires the use of suitable criteria which usually makes the analytical work harder so that numerical techniques must be used. Most existing methods for studying stability switching of equilibria fail when applied to such a class of delay models. To this aim, an efficient criterion for stability switches was recently introduced in [E. Beretta, Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal. 33 (2002) 1144–1165] and extended [E. Beretta, Y. Tang, Extension of a geometric stability switch criterion, Funkcial Ekvac 46(3) (2003) 337–361]. We describe how to numerically detect the instability regions of positive equilibria by using such a criterion, considering both discrete and distributed delay models.     

A THEOREM OF UNIFORMLY ASYMPTOTIC STABILITY FOR DELAY DIFFERENCE SYSTEM

In this paper, we establish a criterion of unformly asymptotic stability for finite delay difference systems in terms of two measures by employing Lyapunov functionals method.     

退化时滞差分系统的通解

讨论具有时滞的退化差分系统，给出其初始函数的相容性条件，并给出其通解，最后举例说明之．     

脉冲耦合时滞微分与连续差分系统的稳定性

该文研究脉冲耦合时滞微分与连续差分系统的稳定性.首先,该文为这类系统引入了一些新的概念如L_2稳定、吸引和L_2渐近稳定,然后给出了一些系统L_2稳定和L_2渐近稳定的判据.该文也给出了一个例子来验证所得结论的有效性.应该注意到这是首次考虑这类脉冲系统.     

退化时滞微分系统解的指数估计

为了更深入地研究退化时滞微分系统,本文应用算子理论和Gronwall引量等,讨论了其解的指数估计问题,并给出指数估计的表达式。     

On qualitative properties of differential-algebraic equations

Linear systems of ordinary differential equations with identically degenerate coefficient matrix before the derivative of the unknown vector function are considered. The structure of general solutions and the notion of singular point of such systems are discussed. From the comparison of the properties of the “perturbed” and original problems, a sufficient criterion for the Lyapunov asymptotic stability of the zero solution is obtained.     

退化时滞微分系统的全时滞稳定性

本文利用复Lyapunov方程给出了退化时滞微分系统全时滞渐近稳定的充要条件。     

具概率延迟反馈金融系统的脉冲控制

研究了概率时滞脉冲金融系统平衡点的全局渐近稳定性问题。首先,通过定义合适的时滞分段区间上的随机变量,给出了概率时滞的脉冲金融系统的数学模型,根据脉冲微分不等式特点构造了一个简便合适的Lyapunov函数利用脉冲微分不等式引理、控制脉冲间隔与脉冲量以及概率时滞分析技巧,获得了较大时滞允许范畴下的平衡点的全局指数稳定,并通过数值实例验证了方法的可行性以及概率时滞的优势。特别地,稳定性判定准则的时滞允许上限的增大,扩大了准则的实用性.     

带有非线性收获和妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支

本文研究了一类同时带有非线性食饵收获和捕食者妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支问题.利用了分支理论和稳定性理论,以捕食者妊娠时滞作为系统的分支参数,获得了所提出的新系统在正平衡点处系统稳定性的相关判据条件和Hopf分支的产生条件.推广了一般带有线性收获和时滞的微分代数捕食者-食饵系统的结论.