多元有理函数系统与电网络
2012-6
高等教育出版社
鲁凯生 著
304
《多元有理函数系统与电网络（英文版）》主要介绍多元有理函数系统与电网络的结构和性质，详细讨论了域F（z）上的矩阵及其特征多项式的可约性条件；定义了I型矩阵并证明了它的两个基本性质；介绍了独立参量的变量代换条件，域F（z）上线性系统的结构能控能观性问题、电网络的结构性质、RLCM网络的可断性和可约性及能控能观性、有源网络状态方程的存在性条件、能控能观性条件等；附录给出了《多元有理函数系统与电网络（英文版）》用到的一些知识。 《多元有理函数系统与电网络（英文版）》适合电子电气、自动化和应用数学（矩阵理论）专业的研究生、科研和工程技术人员参考阅读。
PrefaceAcknowledgments1 IntroductionReferences2 Matrices over Field F（z） of Rational Functions in Multi-parameters2.1 Polynomials over Field F（z） or Ring F（z）[隴2.2 Operations and Determinant of Matrix over F（z）2.3 Elementary Operations of Matrices over F（z） and Some Conclusions2.4 Operation and Canonical Form of Matrix over F（z）2.4.1 Matrix over F（z） and its canonical expression2.4.2 Characteristic matrix2.4.3 Two canonical forms of nonderogatory matrix2.4.4 Rational canonical form and general Jordan canonical form2.5 Reducibility of Square Matrix over F（z）2.6 Reducibility Condition of Class of Matrices over F（z）2.6.1 A class of RFM2.6.2 Some lemmas and definitions2.6.3 Reducibility condition2.6.4 Applications2.6.5 Summary2.7 Two Properties2.7.1 Some lemmas2.7.2 Type-l matrix has two properties2.7.3 Problems2.8 Independent Parameters and a Class oflrreducible Polynomials over F（z） [隴2.9 Conclusions2.10 New Model and Its Reducibility2.10.1 The new model2.10.2 Reducibility conditionReferences3 Controllability and Observability of Linear Systems over F（z）3.1 Controllability and Observability in Time Domain3.1.1 Preliminaries [Lu， 2001]3.1.2 Controllability criteria [Lu， 2001]3.1.3 The canonical decomposition of controllability and observability of systems3.1.4 Criterions to linear physical systems3.1.5 Applications to control systems3.2 Controllability and Observability in Frequency Domain3.2.1 General systems [Lu et al.， 1991]3.2.2 SC-SO of composite systems [Lu et al.， 1991]3.2.3 Polynomial matrix [Liu， 2008] References4 Electrical Networks over F（z）4.1 Resistor-Source Networks over F（z）4.1.1 Introduction4.1.2 General resistor-source networks4.1.3 Unhinged networks4.1.4 Effects of single source4.2 Separability and Reducibility Conditions of RLC Networks over F（z） and Their Applications4.2.1 Introduction4.2.2 Preliminaries4.2.3 Separability condition4.2.4 Separability and reducibility4.2.5 Applications4.3 Controllability and Observability of RLC Networksover F（z）5 Further ThoughtAppendixIndex
