On robust stability of a class of polynomial families

In this paper,we discuss the robust stability of a class of polynomial families more general than the interval polynomial family and diamond polynomial family.We prove that the Hurwitz stability of some special cases of this class of polynomial families can be determined by checking finite polynomials.We also give an example to illustrate that it is not always possible to determine the Hurwitz stability of all this class of polynomial families by checking finite polynomials.     

MINIMAL POLYNOMIAL MATRIX AND LINEAR MULTIVARIABLE SYSTEMS(Ⅰ)

part(Ⅰ)of this work is on the theory of minimal polynomial matrix and Part(Ⅱ)onthe applications of this theory to linear multivariable systems.In Part(Ⅰ).concepts of annihilating polynomial matrix and the minimal polynomialmatrix of a given linear transformation in a vector group are given and the concepts of thegenerating system and minimal generating system of an invariant subspace for a givenlinear transformation are given as well.After discussing the basic properties of theseconcepts the relations between them and the characteristic matrix corresponding to aninduced operator of a given linear transformation in any of its invariant subspace arestudied in detail.The characteristics of the minimal polynomial matrix for a given vectorgroup and the necessary and sufficient condition for the two generating systems to have thesame generating subspace is given.Using these results we can give the expression for the setof all B’s which makes the system x=Ax Bu a complete controllable system for a givenA.     

关于一类多项式族的鲁棒稳定性研究

本文对包括区间多项式族和菱形多项式族的一类多项式族的鲁棒稳定性进行了研究.我们给出并证明了其中几个可用有限检验来判断的多项式族的Hurwitz稳定的实例;同时举例说明了有限检验对所有这一类多项式族并不总是可行的.     

最小多项式矩阵与线性多变量系统(Ⅱ)

本文之(Ⅰ)[8]是关于最小多项式矩阵的理论;其(Ⅱ)是关于这一理论在线性多变量系统中的应用.在本部分的第一节中,我们利用(Ⅰ)中的理论,详细地讨论线性多变量系统输入问题的一些结果.在第二节中,利用对偶性,我们给出行n.p.m.及行生成组等概念,并讨论线性多变量系统输出问题的某些结果.在第三节中.我们讨论化状态空间型为多项式矩阵型的方法.在第四节中,我们讨论这一问题的反问题,即化多项式矩阵型为状态空间型的问题.为说明这些理论和方法,我们给出一些有趣的例子.     

粘性阻尼模型的实模态与复模态解耦法的物理特征

本文是从教学与工程的角度,阐述具有粘性阻尼模型的多个自由度系统两种不同的解耦特性,讨论了两种解耦法的物理意义与几何形象。     

稳定摄动界与厂义Cramer法则

本文分为四部分：１是引言，叙述研究这一问题的意义，特别是对鲁棒分析的意义；２是必要的基本概念与广义Ｃｒａｍｅｒ法则；３，４两部分分别研究了最小∞范数解和最小１范数解的理论和算法，本文所得到的结果不仅对线性代数，而且对鲁棒控制、最优控制和线性规划有意义．     

最小多项式矩阵与线性多变量系统(Ⅰ)

本文分为两部分:(Ⅰ)为关于最小多项式矩阵的理论:(Ⅱ)为最小多项式矩阵理论在线性多变量系统中的应用.在(Ⅰ)中,我们给出了线性变换在向量组的消失多项式矩阵与最小多项式矩阵的概念,给出了不变子空间的生成组与最小生成组的概念.在讨论了这些概念的基本性质之后,我们研究了它们与线性变换在任何不变子空间上诱导算子对应的特征矩阵之间的关系,给出了向量组的最小多项式矩阵类的特征,并给出了有相同生成空间的生成组之间的充分必要条件.利用这些结果,对于给定的矩阵A,给出了能使系统x=Ax+Bu完全可控的矩阵B的全体的集合的表达式.     

MINIMAL POLYNOMIAL MATRIX AND LINEAR MULTIVARIABLE SYSTEM(Ⅱ)

part(Ⅰ) of this work is on the theory of minimal polynomial matrix and Part(Ⅱ)is onthe applications of this theory to linear multivarible systeme.In I of this part,using the theory to Part(Ⅰ),some results about input part of a linearmultivarble system are discussed in detail and in Ⅱ,using duality properties,the conceptsabout row n.p.m.and row generating system,etc.are given. and some results about outputpart of linear multivariable system are discussed, too.In Ⅲ,we discuss the approach whichcan give the polynomial model with less dimension from the state-space model and in Ⅳ wediscuss tha inverse of the problem to give the state-space model from the polynomial model.Some interesting examples are given to explain the theory and the approach.     

复多项式族鲁棒稳定性的边界定理

依据文献[1]的思想和理论,我们曾得出了复系数多项式值映射,D等价等概念和边界定理,棱边定理等结论,这些结论是可以改进的.本文利用文献[1]的思想和方法给出了多项式边界定理的一般形式,改进了文献[2]中的某些结果.利用这一边界定理可以给出已有的关于多项式族鲁棒稳定性定理简洁的证明,同时为有关问题的进一步研究提供了有效的工具.