一类非线性时滞差分方程的稳定性

得到了一类线性非自治时滞差分方程的零解的一致稳定、一致渐近稳定和全局渐近稳定的充分条件.     

非线性随机Pantograph微分方程及其θ-方法的均方渐近稳定性

本文主要研究了非线性随机Pantograph微分方程,讨论了其零解的均方渐近稳定性并给出了零解均方渐近稳定的充分条件.在本文的第三部分,我们将随机θ-方法应用于这类问题,获得了数值解均方渐近稳定条件.     

四阶非线性系统的全局渐近稳定性

运用构造李雅普诺夫函数的方法 ,研究了一类四阶非线性系统的全局渐近稳定性 ,给出了该系统零解全局渐近稳定的充分条件     

非线性控制系统的稳定性分析

通过引入拟奇次近似系统的概念,针对具有拟奇次近似系统的二维系统给出了零解是一致渐进稳定的充分条件.并由算例说明该方法在实际应用中是有效和方便的.     

二阶滞后系统的时滞界限

§1.引言 本文考虑当微分系统的零解为渐近稳定时,使得滞后系统的零解仍为渐近稳定的时滞上限τ_0(0<τ_0≤ ∞)。这里系统的参数均为实常数且τ≥0。 这类问题称为微分系统与微分差分系统之间在稳定性问题中的等价性,当时滞上限τ_0= ∞时,系统(1.2)称为无条件稳定的(即系统的零解对任何τ≥0均为渐近稳     

四阶非线性系统的全局部渐近稳定性

运用构造李雅普诺夫函数的方法,研究了一类四阶非线性系统的全局部渐近稳定性,给出了该系统零解全局渐近稳定的充分条件。     

全局半稳定的三次系统

当每个解都正向趋于零时,本文证明,虽然二次系统的奇点必为渐近稳定,但是在同样的条件下,某些三次系统的奇点能够是不稳定的.     

一类四阶非线性系统的全局渐近稳定性

运用Liapunov第二方法讨论了一类四阶非线性系统的全局渐近稳定性,通过构造出较好的Liapunov函数,获得到了其零解全局渐近稳定的充分性准则,去掉了一般要求Liapunov函数具有无穷大这个较强的条件,并推广了部分文献所研究的非线性系统.     

一个求解约束非线性优化问题的微分方程方法

本文构造的求解非线性优化问题的微分方程方法包括两个微分方程系统,第一个系统基于问题函数的一阶信息,第二个系统基于二阶信息．这两个系统具有性质:非线性优化问题的局部最优解是它们的渐近稳定的平衡点,并且初始点是可行点时,解轨迹都落于可行域中．我们证明了两个微分方程系统的离散迭代格式的收敛性定理和基于第二个系统的离散迭代格式的局部二次收敛性质．还给出了基于两个系统的离散迭代方法的数值算例,数值结果表明基于二阶信息的微分方程方法速度更快．     

具有扰动的非自治中立型泛函微分方程的渐近稳定性

本文讨论了具有扰动的非自治中立型泛函微分方程的3/2-稳定性,得到了零解一致稳定和渐近稳定的充分条件.     

A quantitative study on the stability of delay discrete singular systems

For quadratic delay discrete singular systems, an algebraic criterion on the stability is established, and the size of the uniform stability region and asymptotic stability region around zero is estimated. Hence, the criterion is both qualitative and quantitative. With the computer techniques, the criterion dependent of delay is easy test and applies to the application in the practice. An illustrative simulation is given to illustrate the application of the obtained result.     

STABILITY OF TIME VARYING SINGULAR DIFFERENTIAL SYSTEMS WITH DELAY

In this paper, stability of time varying singular differential systems with delay is considered. Based on variation formula and Gronwall-Bellman integral inequality, we obtain the exponential estimation of the solution and the sufficient conditions under which the considered system is stable and exponentially asymptotically stable. These results will be very useful to further research on Roust stability and control design of uncertain singular control systems with delay.     

Asymptotic stability of solutions of a class of systems of nonlinear differential equations with delay

We study systems of differential equations with delay whose right-hand sides are represented as sums of potential and gyroscopic components of vector fields. We assume that in the absence of a delay zero solutions of considered systems are asymptotically stable. By the Lyapunov direct method, using the Razumikhin approach, we prove that in the case of essentially nonlinear equations the asymptotic stability of zero solutions is preserved for any value of the delay.     

Two-sided estimates for solutions to the Cauchy problem for Wazewski linear differential systems with delay

The Cauchy problem is considered for Wazewski linear differential systems with finite delay. The right-hand sides of systems contain nonnegative matrices and diagonal matrices with negative diagonal entries. The initial data are nonnegative functions. The matrices in equations are such that the zero solution is asymptotically stable. Two-sided estimates for solutions to the Cauchy problem are constructed with the use of the method of monotone operators and the properties of nonsingular M-matrices. The estimates from below and above are zero and exponential functions with parameters determined by solutions to some auxiliary inequalities and equations. Some estimates for solutions to several particular problems are constructed.     

离散多时滞广义不确定系统的变结构控制

研究了线性离散多时滞广义不确定系统的变结构控制的综合与设计问题.首先引入了一种新的受限系统等价分解形式,把所给的系统分解成两个低维的子系统:一个是不带控制项的差分系统;一个是带有控制项的差分系统.其次,根据上面的分解形式及离散时滞广义系统鲁棒稳定性的有关结果,设计了带有差分补偿器的切换函数,使得系统在准切换流形上的运动渐近稳定.然后在不确定项有界的条件下,设计了离散变结构控制律,使得在此控制律的作用下,系统从状态空间中任意一点出发的解的轨迹,于有限步内或者到达准切换流形,此后在准切换流形上渐近滑向原点;或者进入准切换流形的一个小邻域内,并稳定于原点邻域内的一个小的抖振.最后给出了数值例子以说明该综合设计方法的可行性与简便性.     

多时滞线性切换系统的稳定性及其反馈镇定

研究了具有多时滞线性切换系统的稳定性及其反馈镇定问题,利用完备性条件、矩阵分解与二次Lyapunov泛函,给出了多时滞切换系统渐近稳定的充分条件和切换律设计方法.在此基础上,研究了这类系统的镇定控制问题,设计了保证系统时滞独立渐近镇定的控制器.     

Delay-independent stability of homogeneous systems

A class of nonlinear systems with homogeneous right-hand sides and time-varying delay is studied. It is assumed that the trivial solution of a system is asymptotically stable when delay is equal to zero. By the usage of the Lyapunov direct method and the Razumikhin approach, it is proved that the asymptotic stability of the zero solution of the system is preserved for an arbitrary continuous nonnegative and bounded delay. The conditions of stability of time-delay systems by homogeneous approximation are obtained. Furthermore, it is shown that the presented approaches permit to derive delay-independent stability conditions for some types of nonlinear systems with distributed delay. Two examples of nonlinear oscillatory systems are given to demonstrate the effectiveness of our results.     

Robust stability and H∞ control for nonlinear discrete‐time switched systems with interval time‐varying delay

This paper considers the problems of the robust stability analysis and H_∞ controller synthesis for uncertain discrete‐time switched systems with interval time‐varying delay and nonlinear disturbances. Based on the system transformation and by introducing a switched Lyapunov‐Krasovskii functional, the novel sufficient conditions, which guarantee that the uncertain discrete‐time switched system is robust asymptotically stable are obtained in terms of linear matrix inequalities. Then, the robust H_∞ control synthesis via switched state feedback is studied for a class of discrete‐time switched systems with uncertainties and nonlinear disturbances. We designed a switched state feedback controller to stabilize asymptotically discrete‐time switched systems with interval time‐varying delay and H_∞ disturbance attenuation level based on matrix inequality conditions. Examples are provided to illustrate the advantage and effectiveness of the proposed method.     

Cheap control of the time-invariant regulator

The asymptotic solution of the linear quadratic state regulator problem is obtained as the cost of the control tends to zero. Matrix Riccati gains are obtained via singular perturbations theory and are used to asymptotically calculate the optimal control and the corresponding trajectories. Several cases are distinguished and applications are discussed.