广义中立型系统的渐近稳定性

讨论了广义中立型延迟系统理论的渐近稳定性,给出了广义中立型系统渐近稳定的一些充分条件。     

一类两种群随机生态系统的稳定性

利用构造广义二次三项式作为随机李雅普诺夫函数的方法讨论了两种群随机Volterra生态系统的全局渐近稳定性，并对一类特殊情形给出了全局渐近稳定性的充分判据，推广了常微系统已有结果．     

参数变化下的广义指数二分性

本文对时间平移参数系统和时间尺度参数系统给出了广义指数二分性的判据，并且讨论了相应系统的极限方程的广义指数二分性．本文还通过分析广义指数二分性来探讨缓交系数系统和高频振荡系统的渐近稳定性与不稳定性．     

高校应用数学学报第15卷(2000年)B辑(英文版)第2期目次和提要

一类广义系统的渐近稳定性邱卫根　刘永清(华南理工大学自动化系)利用慢子系统判别正则非线性广义系统平衡态X=0的渐近稳定性,给出了系统渐近稳定的判定准则,并给出了例子.具时滞的奇异(n-1,1)共轭边界值问题的多重正解翁佩萱　田艳玲(华南师范大学数学系)使用锥内的不动...     

一类多时滞中立型广义系统的稳定性判据

研究了多时滞的中立型广义时滞系统时滞相关的渐近稳定性问题,利用Lyapunov-Krasovskii泛函,等价模型转换方法和自由由权矩阵的方法,给出了系统时滞相关渐近稳定的充分条件,所给的判据是线性矩阵不等式形式,可方便运用Matlab工具箱求解,最后用一实例验证了方法的有效性。     

双参数对广义Hamilton系统稳定性的影响

研究双参数对带附加项的广义Hamilton系统稳定性的影响.首先将该系统在一定条件下化成梯度系统.其次利用梯度系统的特性来研究这类系统的稳定性及其对双参数的依赖关系.再次在参数平面给出稳定性区域.结果表明,该系统的平衡稳定性随双参数变化可能是稳定的,或渐近稳定的,也可能是不稳定的,相应给出各种稳定性对应的参数变化范围.     

基于比率的广义Holling-Tanner系统的全局渐近稳定性

本文对基于比率的广义Holling-Tanner系统进行了定性分析,给出了系统解有界的条件和平衡点局部稳定的条件．通过构造适当的Liapunov函数,得到了正平衡点全局渐近稳定性的充分条件．     

求解广义中立型系统的线性多步方法的NGP_G-稳定性

建立了广义中立型延迟系统理论解渐近稳定的充分条件 ,分析了用线性多步方法求解广义中立型延迟系统数值解的稳定性 ,在一定的Lagrange插值条件下 ,证明了数值求解广义中立型系统的线性多步方法NGPG_稳定的充分必要条件是线性多步方法是A_稳定的·     

求解广义中立型系统的线性多步方法的NGPG—稳定性

建立了广义中立型延迟系统理论渐近稳定的充分条件,分析了用线性多步方法求解广义中立型延迟系统数值解的稳定性,在一定的Lagrange插值条件下,证明了数值求解广义中立型系统的线性多步方法NGPG－稳定的充分必要条件是线性多步方法的A－稳定的。     

一类广义非线性系统的稳定性与平稳振荡

本文运用广义李雅普诺夫函数方法研究了一类广义非线性系统，给出了其渐近稳定 的判别条件，对相应的周期系统给出了其平稳振荡定理．     

广义大系统的Lyapunov稳定性分析

广义大系统的稳定性是一个非常重要的问题 ,由于广义大系统的复杂性 ,对其稳定性的研究也是一件相当困难的事情 .本文利用 Lyapunov方程 ,应用 Lyapunov函数法 ,研究了广义线性大系统和广义非线性大系统的稳定性和不稳定性 ,得到了系统的关联稳定参数域和不稳定域 .给出例子说明该方法的可行性 .     

Friedrichs Method in a Lyapunov Problem

By using the well-known Friedrichs extension and some a priori inequality, we obtain weak solutions of a Lyapunov equation. In particular, we show that the Lyapunov functions satisfying necessary and sufficient conditions in the domain of asymptotic stability of a singular point some dynamical system must be absolutely continuous.     

时滞广义时变系统的容许性分析与镇定

研究了时滞广义时变系统的容许性与镇定性问题.首先,基于广义Lyapunov不等式、线性矩阵不等式和受限等价方法,建立时滞广义时变系统的Lyapunov不等式,将时滞广义时变系统的容许性问题转化为求解时滞广义时变系统的Lyapunov不等式问题,得到了系统容许的充分条件.然后,根据充分条件进一步研究了时滞广义时变系统的镇定问题,给出了状态反馈镇定器的设计方法.最后,通过数值算例验证了所得结论的有效性.     

Lyapunov reducibility and stabilization of nonstationary systems with an observer

For a linear nonstationary control system with an observer, we assume that the coefficients are locally Lebesgue integrable and integrally bounded on ℝ and construct a linear feedback such that the closed-loop plant-controller system is Lyapunov reducible to the special triangular form corresponding to an independent shift of the diagonal coefficients in the original system and in the system of asymptotic estimation of the state by an arbitrary pregiven quantity. For a periodic system, we prove that the constructed controls and Lyapunov transformation are periodic. We obtain corollaries on the uniform stabilization and global controllability of the central and singular exponents of the system.     

Regular and singular periodic perturbations of an oscillator with cubic restoring force

The paper considers small periodic regular and singular perturbations of a system, whose conservative part is an oscillator with cubic restoring force. The smallness of perturbations is due to both the smallness of the neighborhood of equilibrium and the presence of a small parameter. In the absence of a small parameter, we obtain conditions for Lyapunov stability of the equilibrium position. If a small parameter is present, we derive (both for regular and singular perturbations) an equation whose positive roots are in correspondence with invariant two-dimensional tori of the perturbed system.     

The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects

In this paper we consider the singular value decomposition (SVD) of a fundamental matrix solution in order to approximate the Lyapunov and exponential dichotomy spectra of a given system. One of our main results is to prove that SVD techniques are sound approaches for systems with stable and distinct Lyapunov exponents. We also show how the information which emerges with the SVD techniques can be used to obtain information on the growth directions associated to given spectral intervals.     

Lyapunov exponents of free operators

Lyapunov exponents of a dynamical system are a useful tool to gauge the stability and complexity of the system. This paper offers a definition of Lyapunov exponents for a sequence of free linear operators. The definition is based on the concept of the extended Fuglede-Kadison determinant. We establish the existence of Lyapunov exponents, derive formulas for their calculation, and show that Lyapunov exponents of free variables are additive with respect to operator product. We illustrate these results using an example of free operators whose singular values are distributed by the Marchenko-Pastur law, and relate this example to C.M. Newman's “triangle” law for the distribution of Lyapunov exponents of large random matrices with independent Gaussian entries. As an interesting by-product of our results, we derive a relation between the extended Fuglede-Kadison determinant and Voiculescu's S-transform.     

不确定广义系统的鲁棒稳定界

讨论了不确定广义系统的鲁棒稳定界问题 .利用奇异值分解方法和求解 Lyapunov方程 ,在一定条件下给出了使不确定广义系统正则、无脉冲且稳定的一个稳定界 .实例说明了上述方法的可行性 .     

Geometric Criterium in the Center Problem

In this paper, we use a geometric criterium based on the classical method of the construction of Lyapunov functions to determine if a differential system has a focus or a center at a singular point. This criterium is proved to be useful for several examples studied in previous works with other more specific methods.     

分数阶线性退化微分系统有限时间镇定性问题

本文通过构造新的Lyapunov函数,利用线性矩阵不等式(LMI)和广义Gronwall不等式,研究了分数阶线性退化微分系统的有限时间镇定性问题.充分考虑退化和扰动对系统稳定性的影响,给出了在状态反馈控制器作用下,分数阶退化微分系统在有限时间内镇定的充分条件.并通过两个例子验证了定理条件的可行性.