差分系统的渐近稳定性定理及渐近稳定性区域

本文首先给出了一个利用构造Liapunov函数来判别差分系统渐近稳定性的定理,此定理改进了已有结论[1]且在应用上更为方便.然后,给出了对于自治差分系统,求其渐近稳定区域或吸引区域的几个定理.     

一类含无界时滞的非线性系统的渐近稳定性

基于泛函微分方程的稳定性理论,首先通过构造Lyapunov泛函,再利用矩阵不等式的性质和范数的定义判定矩阵的正定性和负定性.对一类含无界时滞的非线性系统的渐近稳定性问题,作进一步的探讨.     

Asymptotic Stability of Neutral Systems with Multiple Delays

In this paper, the stability analysis problem for linear neutral delay-differential systems with multiple time delays is investigated. Using the Lyapunov method, we present new sufficient conditions for the asymptotic stability of systems in terms of linear matrix inequalities, which can be solved easily by various convex optimization algorithms. Numerical examples are given to illustrate the application of the proposed method.     

具有时滞的周期Lotka-Volterra型系统的全局渐近稳定性

考虑一般具有时间依赖时滞和连续分布时滞的Ｎ－种群周期Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ型系统。通过使用Ｌｉａｐｕｎｏｖ函数方法得到了关于正周期解的存在性和全局渐近稳定性的充分条件。这些条件改进和推广了最近被Ｗａｎｇ,Ｃｈｅｎ,Ｌｕ「２」和Ａｈｌｉｐ,Ｋｉｎｇ「４」得到的相应结果。     

扰动系统的Lipschitz稳定性和指数渐近稳定性

本文给出若干扰动微分系统的零解是一致Ｌｉｐｓｃｈｉｔｚ稳定和指数渐近稳定，以及第五个解渐近地趋于零的一些充分条件。     

脉冲控制系统的渐近稳定性分析

由于脉冲控制系统响应速度快,有较强的鲁棒性和抗干扰能力等特点,因而被广泛研究.但当前对脉冲量为线性函数时的系统稳定性研究较多,而对脉冲量为其它形式时的系统稳定性研究较少.本文对脉冲控制系统的脉冲量是非线性向量值函数,线性与非线性和的向量值函数以及可变的线性向量值函数这三种情形的系统稳定性进行研究,给出了它们稳定性的充分条件.最后,给出数值示例说明所得结果.     

非自治系统渐近稳定的充分条件

本文对 Liapunov关于渐近稳定性的基本定理进行改进 ,在附加辅助函数前提下 ,同时放宽了 V正定 ,有无穷小上界 .V负定的条件 .改进了文 [1 ]～ [6]相应结果     

线性时变切换系统的渐近稳定性研究

考虑一类线性时变切换系统的渐近稳定性.基于矩阵测试理论,文中给出线性时变切换系统在周期切换和等时切换下渐近稳定的充分条件,并通过仿真实例说明结论是正确的.     

Frequency-Domain Criterion for the Global Stability of Dynamical Systems with Prandtl Hysteresis Operator

In the present paper, dynamical systems with Prandtl hysteresis operator are considered. For the class of dynamical systems under consideration, a frequency-domain global stability criterion is formulated and proved. For a second-order dynamical system with Prandtl operator, we demonstrate the advantage of the obtained criterion as compared to the well-known criterion derived by Logemann and Ryan.     

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.     

一类非线性中立型系统的渐近稳定性

基于李雅普诺夫泛函方法,本文讨论了一类非线性中立型系统渐近稳定性的充分条件,推广了中立型系统稳定性结果。最后,通过实例及其仿真数值模拟验证了上述理论结果。     

反应扩散系统双稳波前解的全局渐近稳定性

该文研究一类拟单调反应扩散系统的古典解的渐近行为.在双稳的假定下,利用上、下解方法和单调半流的收敛性结果,证明了当系统的初值在±∞处的极限分别"大于"和"小于"其中间平衡点时,初值问题的解收敛于一个连接两个稳定平衡点的波前解.最后,将结果应用到一个传染病模型.     

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．     

Criteria for the Asymptotic Stability of Solutions of Dynamical Systems

We present a new proof for criteria for the asymptotic stability of systems of difference and differential equations based on the properties of monotone operators in a semiordered space. We also establish necessary and sufficient conditions for the asymptotic stability of stochastic systems of differential and difference equations in the mean square.     

线性离散大系统的稳定性

本文直接运用线性范数型Liapunov函数处理线性定常和时变离散大系统的稳定性,得到了渐近稳定若干判别准则.     

On Global Asymptotic Stability of Second Order Nonlinear Differential Systems

This paper investigates the global asymptotic stability of the autonomous planar systems $ \dot {x} = p_2(y)q_2(x)y $ , $ \dot {y} = p_3(y)q_3(x)x + p_3(y)q_4(x)y $ and $ \dot {x} = f_1(x) + h_2(x)y $ , $ \dot {y} = f_3(x) + h_4(x)y $ , under the assumption that all functions involved in the equations are continuous and that the origin is a unique equilibrium. We present necessary and sufficient conditions for the origin to be globally asymptotically stable.     

时变线性系统的渐近稳定性的积分判据(英)

本文研究时变线性系统的渐近稳定性，给出了一类较为适用的积分判据，对它们的有效性和广泛性通过各种类型的例子作了说明．     

一类耗散型电流体动力学方程组自相似解的渐近稳定性

主要考虑一类来源于电流体动力学中的由非线性非局部方程组耦合而成的耗散型系统的初值问题.利用Lorentz空间中广义L~p-L~q热半群估计和广义Hardy-Littlewood-Sobolev不等式,首先证明了该系统在Lorentz空间中自相似解的整体存在性和唯一性,然后建立了自相似解当时间趋于无穷时的渐近稳定性.因为Lorentz空间包含了具有奇性的齐次函数,因次上述结果保证了具有奇性的初值所对应的自相似解的整体存在性和渐近稳定性.