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本文研究非线性中立型有界时滞大系统和非线性中立型无界时滞大系统在C空间中的稳定性,获得了简洁、实用的稳定性代数充分准则。本文还对非线性时滞大系统的稳定性进行了研究,建立起一个高维时滞微分不等式,推广了著名的Halanay时滞微分不等式。 相似文献
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建立了变系数时滞微分差分不等式,并利用此微分差分不等式讨论了一类分离变量有界可变时滞中立型系统的稳定性. 相似文献
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关于中立型逻辑斯谛方程有界正解的研究已有了长足的发展,而无界正解的研究在已有文献中却非常少见。本文利用振动性原理,结合分析方法得到其无界正解的渐近行为,由此建立中立型时滞逻辑斯谛方程无界正解振动的充分与必要条件,所获结果推广了相关文献的结论。 相似文献
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本文研究退化Lurie直接控制时滞系统和退化Lurie间接控制时滞系统的绝对稳定性,基于Lyapunov稳定性理论和线性矩阵不等式得到绝对稳定的判据,即绝对稳定性仅仅依赖于时滞导数的大小.特别地,时滞可以是无界的函数,仿真示例同时说明了此方法的有效性. 相似文献
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研究一类具高阶Laplace算子的非线性脉冲时滞双曲型偏泛函微分方程,利用二阶脉冲时滞微分不等式,得到了该类方程在两类不同边值条件下所有有界解振动的若干充分判据. 相似文献
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研究了变时滞退化Lurie控制系统的绝对稳定性问题.基于Lyapunov稳定性理论,利用线性矩阵不等式方法给出了系统绝对稳定的判别准则.讨论了变时滞退化Lurie直接控制系统和间接控制系统的绝对稳定性,得到绝对稳定性的充分条件仅依赖于时滞导数的大小,且时滞可以是无界函数:最后给出了实例说明本文结果的有效性. 相似文献
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《数学的实践与认识》2017,(20)
针对带有时变有界的不确定中立型时滞系统进行鲁棒控制研究.基于线性矩阵不等式法和交互式凸组合方法,通过构造恰当的李雅普诺夫泛函,适当分割时滞区间,结合积分不等式引理,减少了不确定时变时滞中立型系统相关判据的决策变量,给出闭环系统渐近稳定的充分条件.数值例子验证了该方法的有效性. 相似文献
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一类非线性时滞差分方程解的若干性质 总被引:3,自引:0,他引:3
本文研究了一类非线性时滞差分方程解的有界持久性、全局渐近稳定性以及无界解的存在性,所得结果解决及部分解决了文献「4」提出的两个open问题,包含了文献「6」中相应的结果。 相似文献
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研究了一类时变时滞切换控制系统的动态回馈控制器的设计问题.其中,控制输入具有导数有界的时变时滞.利用多Lyapunov泛函方法,结合不等式的放缩技巧,用线性矩阵不等式(LMI)的形式给出了确保系统渐近稳定的控制器存在的充分条件,同时设计出了相应的有效切换律.最后给出实例说明了本文控制器设计的有效性. 相似文献
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一类Gronwall-Bellman型不等式的统一证明及其推广 总被引:2,自引:0,他引:2
借助一个极普通的比较定理,通过解普通的常微分方程,对一类Gronwall-Bellman型不等式及其推广进行了统一证明,并将其进一步推广.研究表明,这种方法极具实用性,利用这种方法我们可以构建几乎所有这种类型的不等式,从而为解决一类实际问题提供便捷的途径. 相似文献
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杨甲山 《数学物理学报(A辑)》2014,34(2):393-408
研究了时间测度链上一类具正负系数和阻尼项及非线性中立项的二阶变时滞非线性动力方程的振荡性.利用时间测度链上的有关理论及广义Riccati变换,结合大量不等式技巧,建立了该方程若干新的振动准则,这些准则不仅推广和改进了一些已知的结果,而且在时间测度链上统一了二阶非线性时滞阻尼微分方程和二阶非线性时滞阻尼差分方程的振动性质. 相似文献
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Wilhelm Plesken 《Archiv der Mathematik》2009,92(2):111-118
Both the Gauss-Bruhat decomposition and the LU-decomposition of the general linear group over a field are examples of a Thomas
decomposition of systems of polynomial equations and inequations into disjoint triangular systems, a recently rediscovered
method of the nineteen-thirties, applied to the inequation det (A) ≠ 0 for an n × n-matrix of indeterminants. More specifically it is shown that the cells of the two decompositions can be described by determinantal
equations and inequations yielding simple systems in the sense of Thomas of a rather special type, which are called split
and allow counting solutions over any finite field.
Received: 17 March 2008, Revised: 12 August 2008 相似文献
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This paper is concerned mainly with classes (categories) of ordered algebras which in some signature are axiomatizable by a set of inequations between terms (‘varieties’ of ordered algebras) and also classes which are axiomatizable by implications between inequations (‘quasi varieties’ of ordered algebras). For example, if the signature contains a binary operation symbol (for the monoid operation) and a constant symbol (for the identity) the class of ordered monoids M can be axiomatized by a set of inequations (i.e. expressions of the form t≤t'. However, if the signature contains only the binary operation symbol, the same class M cannot be so axiomatized (since it is not now closed under subalgebras). Thus, there is a need to find structural, signature independent conditions on a class of ordered algebras which are necessary and sufficient to guarantee the existence of a signature in which the class is axiomatizable by a set of inequations (between terms in this signature). In this paper such conditions are found by utilizing the notion of ‘P-categories’. A P-category C is a category such that each ‘Hom-set’ C(a,b) is equipped with a distiguished partial order which is preserved by composition. Aside from proving the characterization theorem, it is also the purpose of the paper to begin the investigation of P-categories. 相似文献
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IntroductionAfter the pioneering work of Kermack-McKendrick on SIRS epidemiological models havebeen studied by many authorSll--31. There are some ldnds of disease which are only spread orhave more opportunities to be spread among children, for example, measles, chickenpox andscarlet fever, while others infectious diseases such as gonorrhea, swahilis are spread only amongadults. Consequently, realistic analysis of disease transmission in a population often requiresthe model to include stage … 相似文献
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Dragi? Bankovi? 《Discrete Mathematics》2007,307(6):750-755
In this paper we consider Boolean inequations i.e. the inequations of the form f(X)≠0, where f is a Boolean function. The basic idea in this paper is: the inequation f(X)≠0 means that there exists p such that f(X)=p and p≠0. We give the formula which determines all the solutions of Boolean inequation. 相似文献
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本文提出了将由变分不等方程导出的弹塑性问题的线性互补方程采用凝缩求解的方法,在避免了迭代计算所节省的时间之外又进一步大大节省了计算时间,极大地提高了对大型结构进行弹塑性分析的效率。 相似文献
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《Mathematical and Computer Modelling》1999,29(3):95-100
In this paper, we suggest and analyze a new iterative method for solving monotone mixed variational inequations using the resolvent operator technique. This new method can be viewed as an extension of the extragradient methods for solving the monotone variational inequalities. 相似文献