一类非完整系统的Lagrange定理及其应用

本文研究一类非完整系统平衡位置流形的稳定性问题·利用Ляпунов直接法和稳定性定义将完整系统的Ｌａｇｒａｎｇｅ定理推广到一类非完整保守系统与耗散系统，并对该类非完整系统平衡位置流形的渐近稳定性与耗散力间的关系作了新的表述，最后举例说明定理的应用·     

非线性非完整系统相对于非惯性系动力学的积分理论*

本文建立非线性非完整系统相对于非惯性系动力学的积分理论.首先,由这种相对运动的Routh方程给出系统的第一积分;其次,分别利用系统的循环积分、能量积分降阶运动方程,得到推广的Routh方程和推广的Whittaker方程;再次,建立这类系统运动的正则方程和变分方程,并由第一积分构造系统的积分不变量;然后,给出系统的Poincare-Cartan型积分变量关系和积分不变量.最后,给出一系列推论.     

非齐次时变分胎人口系统的稳定性

本文对非定常人口系统和非定常带迁移人口系统得到了稳定性的较为精确的界限。从而比较完整地解决了一般人口系统稳定性的问题。     

非线性非完整系统Vacco动力学方程的积分方法*

本文给出积分非线性非完整系统Vacco动力学方程的积分方法.首先,将Vacco动力学方程表示为正则形式和场方程形式;然后,分别用梯度法,单分量法和场方法积分相应完整系统的动力学方程,并加上非完整约束对初条件的限制而得到非线性非完整系统Vacco动力学方程的解.     

变质量非完整系统相对于非惯性系的第一积分与积分不变量

本文给出了变质量非完整系统相对于非惯性系的第一积分存在的条件，建立了这类系统的正则方程和变分方程，证明了由第一积分可直接构造系统的积分不变量，并给出一系列推论和一个例子．     

变质量非线性非完整系统的Gibbs-Appell方程

本文首先将Gibbs-Appell方程推广到最一般的变质量非完整系统.得到变质量非线性非完整系统在广义坐标、准坐标下的Gibbs-Appell方程和积分变分原理,最后给出一个例子.     

具有缓变系数的可分离变量系统的运动稳定性

秦元勋、王联、王慕秋研究了具有缓变系数的线性系统解的全局稳定性,李森林和廖晓昕研究了分离变量系统(?)_s(t)=sum from j=1 to n f_(sj)(x_j)的全局稳定性.R.Reissig、G.sa-nsone、R.conti 总结了分离变量系统的部分结果.本文通过具体构造函数来研究系统     

因变量缺失下部分线性变系数模型的稳健估计

本文讨论因变量缺失下部分线性变系数模型在误差项和解释变量都含有异常点时的稳健估计问题。首先用局部加权线性光滑方法得到非参数部分的稳健估计,然后再得到参数部分的估计,并证明参数和非参数估计量的渐近正态性。最后模拟研究有限样本下估计量的表现。     

具有反应扩散项的变时滞复数域神经网络的指数稳定性

该文研究了一类具有反应扩散项的变时滞复数域神经网络的指数稳定性.首先在假设复数域激活函数可分解的情况下,将该系统分解为相应的实部系统和虚部系统.利用矢量Lyapunov函数法和M矩阵理论,得到了确保该系统平衡状态指数稳定性的充分条件.该条件不含有任何自由变量,相对现有结论具有较低的保守性.最后通过一个数值仿真算例验证了所得结论的正确性.     

部分线性测量误差模型的模拟—推断估计

该文研究了部分线性测量误差模型,即无法直接观测非参数部分协变量,只能得到其替代变量的模型.利用局部线性估计并结合模拟-推断的方法(SIMEX)得到参数及非参数的估计,并在适当的条件下,得到了所提估计量的渐近偏差及方差.将该文提出的模拟-推断方法与Liang(2000)的估计方法比较,表明模拟-推断法在处理测量误差问题上的有效性.值得一提的是,模拟-推断方法不需要对非参数部分协变量的分布提出假设.     

Problems of the partial stability and detectability of dynamical systems

The conditions under which uniform stability (uniform asymptotic stability) with respect to a part of the variables of the zero equilibrium position of a non-linear non-stationary system of ordinary differential equations signifies uniform stability (uniform asymptotic stability) of this equilibrium position with respect the other, larger part of the variables, which include an additional group of coordinates of the phase vector, are established. These conditions include the condition for uniform asymptotic stability of the zero equilibrium position of the “reduced” subsystem of the original system with respect to the additional group of variables. Since within the conditions obtained the stability with respect to the remaining unmeasured coordinates of the phase vector remains undetermined or is investigated additionally, partial zero-detectability of the original system occurs in this case, and the conditions obtained supplement the series of known results from partial stability theory. The application of the results obtained to problems of the partial stabilization of non-linear controlled systems, particularly to the problem of stabilizing an asymmetric rigid body relative to an assigned direction in an inertial space, is considered. The partial detectability of linear systems with constant coefficients is also investigated.     

间接控制系统部分变元的绝对稳定性

ｉ）对变量分离型间接控制系统，本文给出其平凡解关于部分变元绝对稳定的充要条件。ｉｉ）对非变量分离型间接控制系统，给出其平凡解关于部分变元绝对稳定的充分条件。     

线性离散系统的部分稳定性

In this paper, we study the partial stability of linear discrete systems by means of Liapunov's functions of quadratic form . We obtain a necessary and sufficient condition for the system being stable with respect to part of variables and generalize Liapunov's equation to the partial stability of linear discrete systems . A method of constructing Liapunov's function of quadratic form for the stability of the systems is given.     

Partial asymptotic stability via limiting equations

In this paper the limiting equations approach is applied to study the stability properties with respect to a part of the state variables for nonautonomous dynamical systems. Sufficient conditions are given for uniform asymptotic eventual strongly partial stability and for uniform asymptotic partial stability. An application of the results is given.     

线性泛函微分方程关于部分变元稳定性的充要条件

本文在引进具有界滞量线性泛函微分方程的Cauchy矩阵的截断矩阵与截断解算子概念的基础上 ,讨论了这类方程关于部分变元各种稳定性的充要条件 .本文包含此类方程相应的关于全体变元稳定性的经典结论为其特例 .     

Partial stability analysis of some classes of nonlinear systems

A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.     

Stabilization of the stationary motions of non-holonomic mechanical systems

The possible stabilization of the unstable stationary motions of a non-holonomic system is studied from the standpoint of general control theory /1, 2/. As distinct from the case previously considered /3/, when forces of a certain structure are applied with respect to both positional and cyclical coordinates, the stabilization is obtained here by applying control forces only with respect to the cyclical coordinates /4/; the control forces may be applied with respect to some or all of the cyclical coordinates, and depend on the positional coordinates, the velocities, and the corresponding cyclical momenta. It is shown that, just as in the case of holonomic systems /5, 6/, depending on the control properties of the corresponding linear subsystem, the stationary motions, whether stable or unstable, can be stabilized, up to asymptotic stability with respect to all the phase variables, or asymptotic stability with respect to some of the phase variables and stability with respect to the remaining variables. The type of stabilization with respect to the given phase variables depends on the Lyapunov transformations which are needed in order to reduce the critical cases obtained to singular cases /7, 8/.     

Stability of solutions to linear impulsive systems of Itô differential equations with aftereffect with respect to initial data in part of variables

The method of model equations is used to study the moment stability of solutions to linear impulsive systems of Itô differential equations with aftereffect with respect to initial data in part of variables. Sufficient conditions of stability are obtained in terms of parameters of these systems.     

具固定脉冲时刻的脉冲微分系统关于部分变元的指数稳定性

研究了具固定脉冲时刻的脉冲微分系统关于部分变元的指数稳定性,得到了保证零解关于部分变元指数稳定的充分条件,并给出了关于部分变元稳定性的一个新的判定准则.最后给出了其相关例子.     

Stability in part of the variables of “partial” equilibria of systems with aftereffect

The problem of stability in part of the variables of a “partial” equilibrium (this means that a given part of the phase vector coordinates is zero) is considered for nonlinear nonstationary systems of functional differential equations with aftereffect. The notions of stability in part of the variables, which admit more general (compared with the known ones) assumptions about the values of the supremum-norm of the components of the initial vector function corresponding to the variables that do not determine the given equilibrium, are introduced. The stability and asymptotic stability conditions of the the type mentioned above are obtained in the context of the method of Lyapunov-Krasovskii functionals; this conditions allow generalization of several well-known results.