关于区间矩阵的稳定性

文献[1]试图给出由端点矩阵的稳定性来保证区间矩阵的稳定性,文[2,3]指出文[1]的主要结果是错的.本文给出了端点矩阵的稳定性在一定条件下可以保证区间矩阵的稳定性,其结果比文[4]更精确,适用范围更大,且对具有分解的区间矩阵给出了其稳定及不稳定的充分条件.     

广播函数B（n）的上界

本文给出关于广播函数B(n)的一个不等式,由此改进了文[1—3]对B(n)的上界的估计。另外,我们构造了几个新的最小广播图mbg(17)和mbg(18)。     

大系统指数稳定性的某些结果

Lyapunov直接方法的关键在于寻求一个满足一定条件的Lyapunov函数(简称为V函数)。而大系统指数稳定性对V函数的要求往往比较苛刻。专著[1]中要求V函数与‖x‖~2同量级(即存在K_1,K_2>0,使得满足K_1‖x‖~2≤V(t,x)≤K_2‖x‖~2),专著[2]中要求V函数与某个K类函数同量级,后者的条件虽然比前者的弱一些,但并未给出论证。本文通过放宽对V函数的要求而给出了几个较一般的结果,使得[1]中的一些主要定理相应地成为它们的简单推论。     

LURIE控制系统的时滞相关绝对稳定性判据

1 引言关于具有时滞的Lurie控制系统的绝对稳定性的讨论已有不少结果[1～4],其绝对稳定性条件有时滞无关条件和时滞相关条件两种.由于时滞无关条件缺少了时滞的信息,因此必然会使其稳定性具有保守性.下面对具有多个时变时滞的Lurie控制系统,利用不同于文献[1]的方法进行讨论,给出系统绝对稳定的时滞相关判据.算例表明,与文献[1]的结果相比本文结果可降低保守性.     

广义离散随机线性系统的最优递推滤波方法(Ⅱ)

本文对文献[1]给出的广义离散随机线性系统最优估计误差协方差阵进行了分析,在一定 条件下得到了误差协方差阵的上界和下界,继而讨论了由文献[1]给出的滤波器的稳定性.     

关于满足[I(x,y)=I(x,I(x,y))] D-蕴涵的解

研究了[I(x,y)=I(x,I(x,y))]方程,[I]为由连续三角模[T]、连续三角余模[S]和强否定[n]生成的D-蕴涵,即[I(x,y)=S(T(n(x),n(y)),y)],给出了满足方程[I(x,y)=I(x,I(x,y))]的解。     

网络拓扑的超能整循环图构造

循环图是一类重要的网络拓扑结构图,在并行计算和分布计算中发挥重要作用。图[G]的能量[E(G)]定义为图的特征值的绝对值之和。具有[n]个顶点的图[G]称为超能图如果图[G]的能量[E(G)>2n-2]。一个图称为循环图,若它是循环群上的Cayley图,即它的邻接矩阵是一个循环矩阵;整循环图是指循环图的特征值全为整数。借助Ramanujans和,利用Euler函数和Mobius函数,讨论了整循环图的超能性。利用Cartesian积图给出了一个构造超能整循环图的方法。     

非线性抛物组具并行本性的某些实用差分格式

§1．引论在[1—5]中，对非线性抛物组具并行本性的一般差分格式已进行了研究，得到差分解的存在性、唯一性、收敛性和稳定性等许多结果．本文将构造一些对实际计算有用的具并行本性的差分格式．对这些差分格式给出一个关于步长的限制条件．与直接从11－－5］中的结论推导出的条件相比，它是比较有意义的改进，即本文所构造的差分格式的时间步长可取为完全显式差分格式的时间步长的至少sk倍（力为任一正整数）．考虑一维、两维和三维非线性抛物组的初边值问题．在一维空间情形，非线性抛物组为X。一Ah！，。，。加。。＋Jkt，。，。＊，在…     

机构运动学的随机过程分析与精度的失效模型

本文根据随机过程理论,给出了机构在平稳和非平稳条件下机构运动学的概率统计模型.并与文[1]的研究结果作了比较,本文所提供的模型比文[1]的更准确.作为推广.我们进一步给出了机构运动精度的失效模型和一算例.本文所提供的方法可以预估各种不同类型的机构在运动条件下的概率特征和可靠度.也为机械系统的随机振动分析和机构精度的随机控制问题作了必要的准备.     

SLL(k)文法及其分析算法的构造

本文继[4]对 Strong LL(k)文法(即 SLL(k)文法)作了较深入的探讨。文中首先给出了SLL(k)文法的充分必要条件,并详细地论述了该条件的可计算性;然后给出 SLL(k)文法分析算法的 Floyd-evans产生式语言(即 PL)表示及其构造算法。 本文所使用的记号在[4]中可以找到,并且本文所说的文法都是指压缩过的上下文无关文法。     

加权T-图活性的进一步研究

本文给出加权Ｔ－图是活网的另一组充分条件，这组条件包含了Ｔｅｒｕｅｌ等对加权Ｔ－图活性分析的结果，方法简单，便于操作。Ｔｅｒｕｅｌ文中研究了加权单回路网为守恒回路时活的一个充分条件，对一般加权Ｔ图活性的判断只限于每个回路是守恒回路的情况。     

Parametric Transformation of Timed Weighted Marked Graphs: Applications in Optimal Resource Allocation

Timed weighted marked graphs are a subclass of timed Petri nets that have wide applications in the control and performance analysis of flexible manufacturing systems. Due to the existence of multiplicities (i.e., weights) on edges, the performance analysis and resource optimization of such graphs represent a challenging problem. In this paper, we develop an approach to transform a timed weighted marked graph whose initial marking is not given, into an equivalent parametric timed marked graph where the edges have unitary weights. In order to explore an optimal resource allocation policy for a system, an analytical method is developed for the resource optimization of timed weighted marked graphs by studying an equivalent net. Finally, we apply the proposed method to a flexible manufacturing system and compare the results with a previous heuristic approach. Simulation analysis shows that the developed approach is superior to the heuristic approach.      

Marking Optimization of Weighted Marked Graphs

Cyclic manufacturing systems can be modeled by marked graphs, which are an elementary class of Petri nets. To model systems with bulk services and arrivals and to reduce the size of the model, weighted marked graphs can be used. An important step when designing these systems is the definition of the number of manufacturing resources to be used in order to reach a given productivity. In terms of timed Petri nets, this is known as the marking optimization problem and consists of reaching a given average cycle time while minimizing a linear combination of markings. In this paper, a necessary and sufficient condition to obtain a feasible solution of the marking optimization problem of weighted marked graphs with deterministic times is established. A fast heuristic solution, based on an iterative process and using simulation, is given. An example and an application to manufacturing systems are presented.     

Design of T-liveness enforcing supervisors in Petri nets

This paper presents a procedure for the design of supervisors that enforce the transitions in a given set T to be live. T-liveness enforcement corresponds to full liveness enforcement when T equals the total set of transitions. Rather than assuming a given initial marking, this procedure generates at every iteration a convex set of admissible initial markings. In the case of full liveness enforcement and under certain conditions also in the case of T-liveness enforcement, the convex set of each iteration includes the set of markings for which liveness/T-liveness can be enforced. When the procedure terminates, and if it terminates, the final convex set contains only markings for which T-liveness can be enforced. Then, the supervisor keeping the Petri net (PN) marking in this convex set can be easily designed using the place invariant based approach. This paper focuses on the fully controllable and observable PNs. Several extensions of the procedure, including to partially controllable and observable PNs, are outlined.     

无冲突Petri网的结构活性判定研究

结构活性作为Petri网的重要结构性质,在Petri网活性判定领域具有较高的研究价值。从Petri网有向回路对结构活性的影响入手,分析与判定无冲突Petri网的结构活性,讨论库所元素及其后置变迁之间是否存在有向回路对Petri网结构活性的影响,研究该类Petri网结构活性判定方法的相关条件与结论,得到无冲突Petri网是满足结构活性的充分必要条件。分析结果表明,该判定方法可在多项式时间内判定无冲突Petri网的结构活性。     

加权T－图的保性变换

Ｐｅｔｒｉ网的保性化简是Ｐｅｔｒｉ例分析的一种重要途径．Ｍａｒａｔａ等对活的和安全的标识Ｔ－图提出了系统的化简运算体系．蒋昌俊对加权Ｔ－图提出了若干种化简运算，这些化商运算能够保持网的结构有界性、守恒性、可重复性和相容性，但未涉及活性和公平性的保持问题．本文提出对加权Ｔ－图的另一类保性化简，这些化简运算可以保持网的结构活性和公平性．     

Minimizing Place Capacities of Weighted Event Graphs for Enforcing Liveness

This paper addresses the problem of minimizing place capacities of weighted event graphs in order to enforce liveness. Necessary and sufficient conditions of the solution existence are derived. Lower bounds of place capacities while preserving liveness are established and a polynomial algorithm is proposed to determine an initial marking leading to these lower bounds while preserving the liveness.

基于M-Petri网的活性研究

文章给出了M－Petri网的概念,并对其活性进行分析,给出了几个判定 M－Petri网活的条件。     

T-网的活性分析及其判断算法

Petri网的活性反映了实际系统的元死锁性.本文讨论了一类结构简单的Petri网-T-网的活性问题,给出了各类T-网的活性判定定理并给出了判定算法.算法主要计算工作是变迁的前序库所集和后继变迁集以及回路的判断,这三个过程实际上是一个树的搜索过程,因此算法易于实现,判定效率也大大提高.