一类延时细胞神经网络的指数周期性与稳定性

细胞神经网络动态行为的研究是细胞神经网络应用的理论基础。对一类具分布延时细胞神经网络,研究了其全局指数周期性与稳定性。在输出函数满足全局Lipschitz连续的条件下,通过构造合适的Lyapunov泛函,给出了延时细胞神经网络全局指数周期性与稳定性的容易验证的充分条件。给出了算例及其仿真结果来验证所得结论,并说明所得结论与文献[16]的结论是相互独立的。     

时滞随机线性大系统的指数稳定性

针对一般随机线性时滞微分方程，给出了方程的平凡解的几乎必然指数稳定性的一个充分条件，由此利用时滞随机系统的比较原理建立一般时滞随机线性大系统的二阶矩指数稳定与几乎必然指数稳定新的代数判据．利用恰当的Lyapunov函数结合不等式技巧得到了这些条件．特别是用一个代数方程给出了依赖时滞的Lyapunov指数的估计．并用实例加以验证．     

基于计算机仿真的控制系统新型稳定性判据

在分析Lyapunov稳定性理论局限性的基础上,提出了一种新型的基于计算机仿真的非线性定常控制系统稳定性分析方法,规范和简化了Lyapunov函数的选择办法,扩展了Lyapunov稳定性理论.将Lyapunov稳定性判据第二法(即直接法)中的有关局部稳定性的充分条件扩展成为充分必要条件.给出了该方法的理论证明,并且将该方法成功地在MATLAB环境下应用于单级倒立摆模糊控制系统的稳定性分析.实验结果证明该方法是有效的.     

不确定脉冲系统的鲁棒指数稳定性分析

对线性和非线性不确定脉冲系统的鲁棒指数稳定性问题进行了研究，利用拟Lyapunov函数法以及Riccati和Hamilton-Jacobi不等式等方法，分别得到了线性和非线性不确定脉冲系统鲁棒指数稳定的充分条件，这些鲁棒指数稳定性判据可用Riccati不等式方程或Hamilton-Jacobi不等式方程是否有正定解检验，最后，给出了一个实例加以验证所得到的结论。     

离散动态系统稳定与不稳定的简捷判据

运用矩阵特征值分析技巧研究了区间矩阵及一类离散动态系统的稳定性问题。在无需任何附加条件的情况下,仅用区间矩阵的界阵元素给出了一般区间矩阵及离散动态系统混合稳定、渐进(离散)稳定与不稳定的简便代数判据(含充分条件、必要条件与充要条件),弃掉了对区间矩阵的下(上)界阵为非负(正)的条件要求。相对于现存结果,提出判据不仅明显具有普适性强实用范围广且保守性小的特性,而且还涵盖了一些原有的稳定性判据。     

灰色时滞离散大系统的稳定性

本文讨论了一类具有时滞的灰色离散大系统的稳定性问题、给这类系统的稳定性研究了提供了一种新的处理办法，获得一些简单的代数判据。     

一个离散时间系统稳定性判据及其应用

给出了一个便于应用的判定离散时间系统稳定性的简单判据，做为实例，分析讨论了某鱼雷在深度控制系统操纵下纵平面运动的稳定性.     

线性不确定多时滞系统的稳定性新判据

针对线性不确定多时滞系统,建立了一个新的时滞无关稳定性充分条件的结果。根据谱半径相关理论,通过频域法,在只要求系统矩阵A为Hurwitz矩阵的条件下,得到了线性不确定多时滞系统的稳定性新判据。最后,通过两个数值示例与已有文献中的结果进行比较,说明了该结果的有效性。     

嵌入式实时调度系统抖动稳定性分析

分析了嵌入式实时调度系统中控制任务的采样周期和延时不规则抖动属性及稳定性能。并且,针对抖动范围有界但抖动属性不能精确已知的离散状态系统,提出一个保守的系统稳定性充分判据。该判据将抖动引起的时变不确定性描述为系统的离散时间闭环区间状态矩阵,利用李雅普诺夫方程和矩阵的无穷范数,导出区间系统鲁棒稳定的充分条件。该方法计算量小且能减小区间代数计算结果易于扩张的问题。仿真算例表明该判据简单有效且能降低保守性。     

非线性微分-代数系统稳定性的几个判据

研究非线性微分－代数系统的稳定性问题,给出利用非线性函数的偏导数矩阵判别非线性微分－代数系统平衡态稳定和不稳定的几个判据,所得结果形式简洁,易于应用．最后利用例子说明所得判据的有效性     

数值求解多延迟中立型系统的渐近稳定性

给出并证明了多延迟中立型系统渐近稳定的克分条件；分析了用线性多步法求解多延迟中立型系统数值解的稳定性，基于Lagrange插值，证明了数值求解多延迟中立型系境的线性多步法渐近稳定的充分必要条件是它是A-稳定的．     

Study on Robust Uniform Asymptotical Stability for Uncertain Linear Impulsive Delay Systems

In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory     

多变量网络控制系统建模与稳定性分析

研究了一类多变量网络控制系统的建模和稳定性问题,基于线性时不变对象,推导了该类网络控制系统的时滞连续时间数学模型,并利用李雅普诺夫第二法,分析了系统的渐近稳定性,得到了系统稳定运行的最大允许时延和全时滞稳定的条件。最后,通过实例仿真分析证实了本文所提理论的有效性,以及稳定判据的可行性。     

Controlling uncertain fuzzy neutral dynamic systems with Markov jumps

The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems (MJSs) with parameters uncertainties and multiple time-delays are considered. The delays are respectively considered as constant and time varying, and the uncertain parameters are assumed to be norm bounded. By means of Takagi-Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By selecting the appropriate Lyapunov-Krasovskii functions, the sufficient condition is given such that the uncertain fuzzy neutral MJSs are stochastically stability for all admissible uncertainties and satisfies the given H∞ control index. The stability and H∞ control criteria are formulated in the form of linear matrix inequalities, which can be easily checked in practice. Practical examples illustrate the effectiveness of the developed techniques.     

STABILITY OF N-DIMENSIONAL LINEAR SYSTEMS WITH MULTIPLE DELAYS AND APPLICATION TO SYNCHRONIZATION

This paper further investigates the stability of the n-dimensional linear systems with multiple delays. Using Laplace transform, we introduce a definition of characteristic equation for the n-dimensional linear systems with multiple delays. Moreover, one sufficient condition is attained for the Lyapunov globally asymptotical stability of the general multi-delay linear systems. In particular, our result shows that some uncommensurate linear delays systems have the similar stability criterion as that of the commensurate linear delays systems. This result also generalizes that of Chen and Moore （2002）. Finally, this theorem is applied to chaos synchronization of the multi-delay coupled Chua＇s systems.     

时滞细胞神经网络的全局渐近鲁棒稳定性分析

针对一类具有时滞的细胞神经网络系统,利用新的Lyapunov Krasovskii函数,给出了系统全局渐近鲁棒稳定的时滞相关稳定性条件。其结果以线性矩阵不等式的形式给出,可以很容易求出系统稳定的时滞上界。进而可以很容易得到时滞无关稳定性结果,且该结果包含了现有文献中许多关于时滞无关稳定性分析的结果。数值算例说明了结论的有效性。     

New results on the robust stability analysis of neural networks with discrete and distributed time delays

Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality （LMIs） technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.     

On delay-dependent robust stability for uncertain neutral systems

1.INTRODUCTION Time delaysarefrequentlyencounteredinvariousengi neeringsystems,includingaircraftstabilization,nuclear reactors,populationdynamicsmodels[1].Theirexistence isoftenthesourceofinstabilityinmanycontrolsystems.Stabilitycriteriafortime delaysystemscanbeclassified intotwocategories.Thestabilitycriteriathatincludein formationonthesizeofdelaysarereferredtoasdelay de pendentcriteria[2～18]andthecriteriaapplicabletoanar bitrarysizeofdelaysarereferredtoasdelay independent criteria[19～…     

Robust stability and stabilization for uncertain discrete-time switched singular systems with time-varying delays

The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated. By constructing a novel switched Lyapunov–Krasovskii functional, a delay-dependent criterion for the unforced system to be regular, causal and uniformly asymptotically stable is established in terms of linear matrix inequalities (LMIs). An explicit expression for the desired memoryless state feedback stabilization controller is also given. The merits of the proposed criteria lie in their less conservativeness and relative simplicity, which are achieved by considering additionally useful terms (ignored in previous methods) when estimating the upper bound of the forward difference of the Lyapunov–Krasovskii functional and by avoiding utilizing any model augmentation transformation. Some numerical examples are provided to illustrate the validity of the proposed methods.     

具有时滞的区间大系统的鲁棒稳定性

应用Lyapunov函数方法讨论了具有时滞的区间大系统的鲁棒稳定性,给出了该系统鲁棒稳定的充分条件,同时还讨论了一类不确定时滞大系统的鲁棒稳定性,最后给出了结果的示例并与前人的结果进行了比较。