《rational function systems and electrical networks with multi-parameters》是2012年6月高等教育出版社出版的圖書，本書主要介紹多元有理函式系統與電網路的結構和性質，詳細討論了域F（z）上的矩陣及其特徵多項式的可約性條件；定義了I型矩陣並證明了它的兩個基本性質。
基本介紹
- 中文名：rational function systems and electrical networks with multi-parameters
- 作者：魯凱生
- 出版社：高等教育出版社
- ISBN：9787040346930
內容簡介,圖書目錄,
內容簡介
《多元有理函式系統與電網路（英文版）》主要介紹多元有理函式系統與電網路的結構和性質，詳細討論了域F（z）上的矩陣及其特徵多項式的可約性條件；定義了I型矩陣並證明了它的兩個基本性質；介紹了獨立參量的變數代換條件，域F（z）上線性系統的結構能控能觀性問題、電網路的結構性質、RLCM網路的可斷性和可約性及能控能觀性、有源網路狀態方程的存在性條件、能控能觀性條件等；附錄給出了《多元有理函式系統與電網路（英文版）》用到的一些知識。
《多元有理函式系統與電網路（英文版）》適合電子電氣、自動化和套用數學（矩陣理論）專業的研究生、科研和工程技術人員參考閱讀。
圖書目錄
Preface
Acknowledgments
1 Introduction
References
2 Matrices over Field F（z） of Rational Functions in Multi-parameters
2.1 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 Conclusions
2.4 Operation and Canonical Form of Matrix over F（z）
2.4.1 Matrix over F（z） and its canonical expression
2.4.2 Characteristic matrix
2.4.3 Two canonical forms of nonderogatory matrix
2.4.4 Rational canonical form and general Jordan canonical form
2.5 Reducibility of Square Matrix over F（z）
2.6 Reducibility Condition of Class of Matrices over F（z）
2.6.1 A class of RFM
2.6.2 Some lemmas and definitions
2.6.3 Reducibility condition
2.6.4 Applications
2.6.5 Summary
2.7 Two Properties
2.7.1 Some lemmas
2.7.2 Type-l matrix has two properties
2.7.3 Problems
2.8 Independent Parameters and a Class oflrreducible Polynomials over F（z） 隴
2.9 Conclusions
2.10 New Model and Its Reducibility
2.10.1 The new model
2.10.2 Reducibility condition
References
3 Controllability and Observability of Linear Systems over F（z）
3.1 Controllability and Observability in Time Domain
3.1.1 Preliminaries [Lu， 2001]
3.1.2 Controllability criteria [Lu， 2001]
3.1.3 The canonical decomposition of controllability and observability of systems
3.1.4 Criterions to linear physical systems
3.1.5 Applications to control systems
3.2 Controllability and Observability in Frequency Domain
3.2.1 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] References
4 Electrical Networks over F（z）
4.1 Resistor-Source Networks over F（z）
4.1.1 Introduction
4.1.2 General resistor-source networks
4.1.3 Unhinged networks
4.1.4 Effects of single source
4.2 Separability and Reducibility Conditions of RLC Networks over F（z） and Their Applications
4.2.1 Introduction
4.2.2 Preliminaries
4.2.3 Separability condition
4.2.4 Separability and reducibility
4.2.5 Applications
4.3 Controllability and Observability of RLC Networksover F（z）
5 Further Thought
Appendix
Index
