单滞后区间动力系统的稳定性

本文研究如下单滞后时变区间动力系统ｘ（ｔ）＝Ｎ［Ｐ，Ｑ］ｘ（ｔ）＋Ｎ［Ｃ（ｔ），Ｄ（ｔ）］ｘ（ｔ－τ），τ≥０的渐近稳定性的ａ稳定性，给出了其渐近稳定和ａ稳定的充分条件，推广和改进了文［１，２］的工作。     

关于可正定化矩阵的判定

１．引言众所周知，对于线性代数方程组Ａｘ＝ｆ的许多迭代解法，在系数矩阵Ａ正定时有很好的收敛性定理［１］．我们自然希望把这些定理推广到范围更广的一类矩阵上去．文［２］为此定义了一种可正定化矩阵：若存在对角阵Ｐ和Ｑ使Ａ＝ＰＡＱ为正定阵，则称Ａ为可正定化矩阵，并且把迭代法Ｊａｃｏｂｊ；ＳＯＲ，ＥＰＥｋ等对正定矩阵的收敛性定理推广到可正定化矩阵的情形．于是问题归结为如何判定系数矩阵Ａ是可正定化矩阵．文［２］根据计算机上数的特点，在假定Ａ的元素均为整数且对角线元素为正的前提下，依据整数理论给出了一种方法．…     

时域鲁棒设计的新方法──［P］和［V］·［V~－1］的极小化

本文讨论在极点配置的约束下，使［Ｐ］和［Ｖ］·［Ｖ－１］（条件数）极小化的问题，其中Ｐ是（Ａ＋ＢＦ）＇Ｐ＋Ｐ（Ａ＋ＢＦ）＝－２Ｉｎ的工定解，Ｖ是Ａ＋ＢＦ的特征向量矩阵．两种指标都反映了系统鲁棒稳定的程度．通过定义一矩阵函数并引入新的自由变量Ｕ，可放松极点配置的约束，并能系统的推导［Ｐ］／Ｕ及（［Ｖ］·［Ｖ－１］）／Ｕ，从而将鲁棒设计转化为无约束的梯度法寻优，实例说明，本文设计方法的效果很好．     

一种求多边形平移重叠面积最大值的快速算法

设Ｐ和Ｑ是平面上的２个简单多边形，ｔ∈Ｒ２是平面上任意矢量，多边形Ｐ与Ｑ的平移重叠面积函数定义为Ａｒ（ｔ）＝Ａｒｅａ（Ｐ∩（ｔ＋Ｑ）），这里ｔ＋Ｑ表示Ｑ平移了ｔ后形成的多边形。为快速求解平移重叠面积函数的最大值，本文提出了一种优化计算策略，它包括在全局上组合应用遗传算法和最速上升算法快速搜索函数最大值和在局部上利用修正的扫描线算法来快速计算函数值。     

空值环境下（N）4NF,（N）5NF的研究

本文是在作者已经发表的文［１］，［２］，［３］，［４］的基础上，分别对空值环境下的４ＮＦ，５ＮＦ进行了讨论。给出了空值环境下的４ＮＦ，５ＮＦ的相应定义和有关概念，研究了相关的理论，还给出了分解为（Ｎ）４ＮＦ的分解算法。     

关于文"LQ逆问题研究"的问题讨论

关于文“ＬＱ逆问题研究”的问题讨论傅诒辉（华中理工大学自控系武汉４３００７４）关键词ＬＱ逆问题，加权矩阵，极点配置．文［门定理２给出了连续系统ＬＱ逆问题有解的充分条件以及确定加权矩阵Ｑ和Ｒ的参数化方法．本文构造性地给出了满足文［１］定理２全部条件的参...     

求解混合0-1线性规划问题的一个分支定界算法

１．引言考虑如下的０－１混合线性规划问题列（Ｐ）：其中ｃ，ｄ，ｂ都是己知的具有相应维数的行向量或列向量，Ａ，Ｂ是已知的具有相应行数和列数的矩阵，ｘ是连续变量，ｙ＝（ｙ１，ｙ；...，ｙｎ）Ｔ是０－１变量．为讨论方便，不妨设问题（Ｐ）没有无界的最优值．关于问题（Ｐ）的求解，已经有很多方法，例如割平面方法、分解方法、分支定界方法、隐枚举法［１－３］．由于整数线性规划属于ＮＰ问题，对中等规模和大规模的混合整规划问题尚无成熟可靠的有效方法．本文利用对偶线性规划，构造定界函数，提出求解问题（Ｐ）的一个分支定…     

一个m维整数瓶颈运输问题及其算法

５１．引言 整数瓶颈问题 （ＩＢＰ的研究最早可追朔到 １９５９年Ｇｒｏｓｓ关于瓶颈指派问题 （ＢＡＰ的研究［’］以及 Ｂａｒｓｏｗ关于时间运输问题（ＴＴＰ）的研究［’］．对 ＢＡＰ相继又出现了改进算法［３］、图算法［４］以及将其化为一般指派问题的算法［’］． １９６９年以来， Ｈａｍｍｅｒ等人又研究了 ＴＴＰ［６－８１．近十几年来，对 ＩＢＰ仍有一些新成果面世 ［９－１５１．但无论国内或者国外，所有成果其目标函数均局限在１，２维的简单情形．本文提出并研究了目标函数为。维的整数瓶颈运输问题， ５２．问题的提出…     

对"评热防护发汗冷却控制一文"的评论

对“评热防护发汗冷却控制一文”的评论＠杨学实对“评热防护发汗冷却控制一文”的评论杨学实（北京１４２信箱２０６分箱北京１００８５４）文献［２］认为文献［１］的方程（４）即Ｔｔ＝α２Ｔｙ２＋βＴｙ＋ｓ（ｔ）ｌ－ｙＴｌ－ｓ（ｔ）ｙ（１）的右端第三...     

Athlon XP的技术规格

首先，这款新处理器的名字［ＡｔｈｌｏｎＸＰ］，并不只是跟随着微软（Ｍｉｃｒｏｓｏｆｔ）的新操作系统ＷｉｎｄｏｗｓＸＰ的潮流（像ＮＶＩＤＩＡ的新驱动程序原本也叫做ＤｅｔｏｎａｔｏｒＸＰ）。在ＷｉｎｄｏｗｓＸＰ中 ＸＰ代表的是惭的体验（ｅｘｐｅｒｉｅｎｃｅ）」，而 ＡｔｈｌｏｎＸＰ中的 ＸＰ还代表着「更高的性能（ｅｘｔｅｎｄｅｄ ｐｅｒｆｏｒｍａｎｃｅ）」。新功能 ＡｔｈｌｏｎＸＰ和先前采用雷鸟（Ｔｈｕｎｄｅｒｂｉｒｄ）核心的桌上型Ａｔｈｌｏｎ比起来，的确快上了３到７％，因为它采用的是新的Ｐａｌｏｍｉｎ…     

Impulsive control of unstable neural networks with unbounded time-varying delays

This paper considers the impulsive control of unstable neural networks with unbounded time-varying delays, where the time delays to be addressed include the unbounded discrete time-varying delay and unbounded distributed time-varying delay. By employing impulsive control theory and some analysis techniques, several sufficient conditions ensuring μ-stability, including uniform stability, (global) asymptotical stability, and (global) exponential stability, are derived. It is shown that an unstable delay neural network, especially for the case of unbounded time-varying delays, can be stabilized and has μ-stability via proper impulsive control strategies. Three numerical examples and their simulations are presented to demonstrate the effectiveness of the control strategy.     

New stability criteria for neutral-type Cohen–Grossberg neural networks with discrete and distributed delays

This paper studies the existence, uniqueness and globally robust exponential stability for a class of uncertain neutral-type Cohen–Grossberg neural networks with time-varying and unbounded distributed delays. Based on Lyapunov–Krasovskii functional, by involving a free-weighting matrix, using the homeomorphism mapping principle, Cauchy–Schwarz inequality, Jensen integral inequality, linear matrix inequality techniques and matrix decomposition method, several delay-dependent and delay-independent sufficient conditions are obtained for the robust exponential stability of considered neural networks. Two numerical examples are given to show the effectiveness of our results.     

Delay-dependent robust stability analysis of uncertain stochastic neural networks with discrete interval and distributed time-varying delays

This paper is concerned with stability analysis problem for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some numerical examples and comparisons are provided to show that the proposed results significantly improve the allowable upper and lower bounds of delays over some existing results in the literature. Furthermore, the supplementary requirement that the time derivative of discrete time-varying delays must be smaller than the value one is not necessary to derive the results in this paper.     

Robust stability criteria for uncertain stochastic neural networks of neutral-type with interval time-varying delays

This paper deals with the robust stability problem of uncertain stochastic neural networks of neutral-type with interval time-varying delays. The uncertainties under consideration are norm-bounded, and the delay is assumed to be time-varying and belongs to a given interval. By using the Lyapunov-Krasovskill functional method and the linear matrix inequality (LMI) technique, the novel stability criteria are derived in terms of LMI. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed criteria.     

New stability conditions for uncertain T-S fuzzy systems with interval time-varying delay

This paper focuses on the stability problem for uncertain T-S fuzzy systems with interval time-varying delay. The system uncertainties are assumed to be time-varying and norm-bounded. The time-varying delay is considered as either being differentiable uniformly bounded with delay-derivative bounded by constant interval, or being fast-varying case with no restrictions on the delay derivative. Since we employ a novel Lyapunov-Krasovskii functional (LKF) which contains the information on the time-varying delay, and estimate the upper bound of its derivative less conservatively and adopt the convex optimization approach, some less conservative delay-derivative-dependent stability conditions are obtained in terms of linear matrix inequalities (LMIs), without using any free weighting matrix. These conditions are derived that depends on both the upper and lower bounds of the delay derivatives. Finally, some numerical examples are given to demonstrate the effectiveness and reduced conservatism of the proposed method.     

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.     

Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations

In this paper, we study a general class of neural networks with discrete and distributed time-varying delays, whose neuron activations are discontinuous and may be unbounded or nonmonotonic. By using the Leray-Schauder alternative theorem in multivalued analysis, matrix theory and generalized Lyapunov-like approach, we obtain some sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the periodic solution. Moreover, when all the variable coefficients and time delays are real constants, we discuss the global convergence in finite time of the neural network dynamical system. Our results extend previous works not only on discrete and distributed time-varying delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete and distributed time-varying delayed neural networks with discontinuous activations. Two numerical examples are given to illustrate the effectiveness of our main results.     

Novel passivity criteria for neural networks with discrete and unbounded distributed time-varying delays

Novel passivity criteria are presented for the passivity of a class of cellular neural networks with discrete and unbounded distributed time-varying delays. Two types of uncertainty are considered: one is time-varying structured uncertainty while the other is interval uncertainty. The Gu's discretized Lyapunov–Krasovskii functional method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz–Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for passivity of delayed neural networks. A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing passivity criteria.     

New stability criteria for linear systems with interval time-varying delay

This paper investigates robust stability of uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and is a fast time-varying function. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. A new Lyapunov-Krasovskii functional, which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to drive some new delay-dependent stability criteria. In order to obtain much less conservative results, a tighter bounding for some term is estimated. Moreover, no redundant matrix variable is introduced. Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.     

Robust Stability Analysis for Interval Cohen–Grossberg Neural Networks With Unknown Time-Varying Delays

In this paper, robust stability problems for interval Cohen–Grossberg neural networks with unknown time-varying delays are investigated. Using linear matrix inequality, $M$ -matrix theory, and Halanay inequality techniques, new sufficient conditions independent of time-varying delays are derived to guarantee the uniqueness and the global robust stability of the equilibrium point of interval Cohen–Grossberg neural networks with time-varying delays. All these results have no restriction on the rate of change of the time-varying delays. Compared to some existing results, these new criteria are less conservative and are more convenient to check. Two numerical examples are used to show the effectiveness of the present results.