一类不连续系统的W-渐近稳定分析

近年来,集合稳定性问题得到广泛研究.研究一类非线性不连续系统在Filippov解意义下的W-渐近稳定问题.首先,给出这类系统W-稳定相关定义.其次,建立了此类系统实现W-渐近稳定的Lyapunov定理.最后,研究了该系统的静态量化反馈镇定问题,即使用静态量化器实现系统W-渐近稳定.     

脉冲耦合时滞微分与连续差分系统的稳定性

该文研究脉冲耦合时滞微分与连续差分系统的稳定性.首先,该文为这类系统引入了一些新的概念如L_2稳定、吸引和L_2渐近稳定,然后给出了一些系统L_2稳定和L_2渐近稳定的判据.该文也给出了一个例子来验证所得结论的有效性.应该注意到这是首次考虑这类脉冲系统.     

一类非定常经济系统的Lyapunov稳定性

讨论了一类非定常经济系统的Lyapunov稳定性,给出了经济系统稳定和渐进稳定的充分条件和稳定的必要条件,同时得到与系统稳定性有关的临界积累率的解析表达式.结果可为经济政策的制定提供理论依据.     

线性不确定系统的稳定控制鲁棒界和多级稳定鲁棒控制

利用李雅普诺夫稳定性理论研究了线性不确定系统的稳定鲁棒控制问题,得到结果“任何一个稳定控制都是具有一定稳定鲁棒界的稳定控制”.进一步地,根据系统的不确定量的范围,设计了多级稳定鲁棒控制策略.最后给出一个例子说明设计步骤的可行性.     

弱耦合双自由度线性非自治随机系统的准确定稳定条件

讨论了参数激励下的二阶振动系统准确定稳定的充分条件.假设该系统由二个弱耦合的子系统所组成,外加激励作用是稳定的遍历性随机过程.使用二次型性质,得到该系统的特征值边界,以及封闭形式的准确定稳定的充分条件.     

复合随机时滞系统的全局稳定

本文主要是研究了具有时滞随机复合系统的反馈律和全局稳定,及其所需要的充分条件.主要的方法是:引入一个测度函数u,使得关于ξ的随机系统稳定,再通过附加条件,从而达到整个复合系统的稳定.     

R(O)SSLER系统平衡点集的镇定

研究了R\"ossler系统的镇定问题. 当参数变化时, R\"ossler系统具有两条平衡点曲线, 因此是一个多平衡点系统. 在这些平衡点中, 有的是不稳定, 有的平衡点上会出现Hopf分岐.提出了一种多项式反馈控制律, 保证R\"ossler系统的两平衡点曲线上的平衡点都渐近稳定. 现有的方法只能保证某个参数点附近平衡点渐近稳定.     

矩阵系统的稳定与条件稳定

一个矩阵对应一种状态变换 .一系列的矩阵构成矩阵序列系统 .任一微小的扰动都会破坏伪逆的精确性 ,即状态的最后结果 .本文证明 :若矩阵系统是广义各态历经的 ,则系统是稳定的 ;若矩阵系统是普真的 ,则系统是条件稳定的 .     

一类随机系统的有限时间镇定

讨论随机系统的有限时间镇定问题.首先提出了随机系统有限时间稳定的概念;其次证明了随机系统有限时间稳定的Lyapunov定理;然后,讨论了一类随机系统的镇定问题.     

滑动轴承转子系统动力学稳定域的数值分析方法

根据Floquet理论定义了非线性非自治系统周期解的稳定度.从动力系统流的概念出发,给出利用非线性非自治系统稳态周期解受扰后的瞬态响应,计算周期解稳定度的数值计算方法.以稳定度等于零为临界判据,分析计算了滑动轴承平衡和不平衡刚性转子系统的稳定吸引域.研究发现,平衡转子随着转速的升高稳定域减小;不平衡转子随着不平衡量的增大稳定域减小;且工频周期解的稳定域比同样系统条件下平衡点的稳定域小.     

Characterization of polynomial decay rate for the solution of linear evolution equation

In this paper, we study the decay rate of solutions to strongly stable, but not exponentially stable linear evolution equations. It is known that the resolvent operator of such an equation must be unbounded on the imaginary axis. Our main result is an estimate of the decay rate when the unboundedness is of polynomial order. We then apply our main theorem to three strongly stable but not exponentially stable systems to obtain the decay rate, which is not available in the literature.Received: July 21, 2003     

Rings of almost unit stable rank 1

We introduce the notion of a ring of almost unit stable rank 1 as a generalization of the notion of a ring of unit stable rank 1. We prove that a ring of almost unit stable rank 1 with nonzero Jacobson radical is a ring of unit stable rank 1 and is a 2-good ring. We introduce the notion of almost 2-good ring and show that an adequate domain is an almost 2-good ring.     

基于Leslie模型的资源持续利用

传统的Leslie模型是具有年龄结构种群演化的有效研究方法.基于持续收获状态的均匀收获是生物资源可持续利用的重要手段.对均匀收获状态下种群保持稳定的条件进行了研究,证明了均匀收获下稳定状态的充要条件,同时基于该条件,给出了临界稳定状态的判定方法,并就临界稳定状态下种群的分布情况进行了研究.通过引入实际数据并就实际数据进行计算,对该判定条件及最终的种群分布情况进行了实证分析.     

Stable multi-sets

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets.  For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable multi-sets and conditions for them to be facet defining are determined.  The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets emerge as an important substructure in the design of optical networks. Received: February 14, 2001/Revised version: September 7, 2001     

Strong stability and the incompleteness of stable models for λ-calculus

We prove that the class of stable models is incomplete with respect to pure λ-calculus. More precisely, we show that no stable model has the same theory as the strongly stable version of Park's model. This incompleteness proof can be adapted to the continuous case, giving an incompleteness proof for this case which is much simpler than the original proof by Honsell and Ronchi della Rocca. Moreover, we isolate a very simple finite set, , of equations and inequations, which has neither a stable nor a continuous model, and which is included in and in , the contextual theory induced by the set of essentially λI-closed terms. Finally, using an approximation theorem suitable for a large class of models (in particular stable and strongly stable non-sensible models like and ), we prove that and are included in , giving an operational meaning to the equality in these models.     

Reduction of Matrices over Bezout Rings of Stable Rank not Higher than 2

We prove that a commutative Bezout ring is an Hermitian ring if and only if it is a Bezout ring of stable rank 2. It is shown that a noncommutative Bezout ring of stable rank 1 is an Hermitian ring. This implies that a noncommutative semilocal Bezout ring is an Hermitian ring. We prove that the Bezout domain of stable rank 1 with two-element group of units is a ring of elementary divisors if and only if it is a duo-domain.     

迹稳定秩一的C~*-代数

本文引入了一类迹稳定秩一的C*-代数,证明了迹稳定秩一的C*-代数与AF-代数的张量积是迹稳定秩一的,得到了一个可分的单的有单位元的迹稳定秩一的,并且具有SP性质的C*-代数是稳定秩一的.同时,还讨论了迹稳定秩一的C*-代数的K-群的某些性质.     

Compact leaves of structurally stable foliations

We prove that any compact manifold whose fundamental group contains an abelian normal subgroup of positive rank can be represented as a leaf of a structurally stable suspension foliation on a compact manifold. In this case, the role of a transversal manifold can be played by an arbitrary compact manifold. We construct examples of structurally stable foliations that have a compact leaf with infinite solvable fundamental group which is not nilpotent. We also distinguish a class of structurally stable foliations each of whose leaves is compact and locally stable in the sense of Ehresmann and Reeb.     

发射物体到指定位置的稳健性参数设计

发射物体到指定位置的稳健性参数设计是稳健性设计中的经典例子之一,也是导弹控制理论中的一个常用模型.但就是对这个经典例子,许多教科书给出的并非最优解.用创立的求解稳定中心的方法(称为全局-局部分析方法或者GL算法Global-Local Algorithm),得出了比历史上更好的稳定中心,并由此引出了许多哲学层面的问题.