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Rational Function Systems and Electrical Networks with Multi-parameters

样章
作者：
Kai-Sheng Lu
定价：
69.00元
ISBN：
978-7-04-034693-0
版面字数：
450.000千字
开本：
16开
全书页数：
304页
装帧形式：
精装
重点项目：
暂无
出版时间：
2012-06-29
物料号：
34693-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
电气工程
三级分类：
电力系统及其自动化

本书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1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；附录给出了本书用到的一些知识。

本书适合电子电气、自动化和应用数学（矩阵理论）方向的研究生、科研和工程技术人员参考阅读。

To overcome the problems of system theory and network theory over real field, this book uses matrices over the field F(z) of rational functions in multi-parameters describing coefficient matrices of systems and networks and makes systems and network description over F(z) and researches their structural properties: reducible condition of a class of matrices over F(z) and their characteristic polynomial; type-1 matrix and two basic properties; variable replacement conditions for independent parameters; structural controllability and observability of linear systems over F(z); separability, reducibility, controllability, observability and structural conditions of networks over F(z), and so on. This book involves three subjects: systems, networks and matrices over F(z), which is an achievement of interdisciplinary research.

  • Front Matter
    • 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)[\lambda ]
    • 2.2 OperationsAnd Determinant of Matrix over F(z)
    • 2.3 Elementary Operations of Matrices over F(z)And Some Conclusions
    • 2.4 OperationAnd 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 formAnd general Jordan form
    • 2.5 Reducibility of Square Matrix over F(z)
    • 2.6 Reducibility Condition of Class of Matrices over F(z)
      • 2.6.1A class of RFM
      • 2.6.2 Some lemmasAnd definitions
      • 2.6.3 Reducibility condition
      • 2.6.4Applications
      • 2.6.5 Summary
    • 2.7 Two Properties
      • 2.7.1 Some lemmas
      • 2.7.2 Type-1 matrix has two properties
      • 2.7.3 Problems
    • 2.8 Independent ParametersAndA Class of Irreducible Polynomials over F(z)[\lambda ]
    • 2.9 Conclusions
    • 2.10 New ModelAnd Its Reducibility
      • 2.10.1 The new model
      • 2.10.2 Reducibility condition
    • References
  • 3 ControllabilityAnd Observability of Linear Systems over F(z)
    • 3.1 ControllabilityAnd Observability in Time Domain
      • 3.1.1 Preliminaries [Lu, 2001]
      • 3.1.2 Controllability criteria [Lu, 2001]
      • 3.1.3 The canonical decomposition of controllabilityAnd observability of systems
      • 3.1.4 Criterions to linear physical systems
      • 3.1.5Applications to control systems
    • 3.2 ControllabilityAnd Observability in Frequency Domain
      • 3.2.1 General systems [Lu etAl., 1991]
      • 3.2.2 SC-SO of composite systems [Lu etAl., 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 SeparabilityAnd Reducibility Conditions of RLC Networks over F(z)And TheirApplications
      • 4.2.1 Introduction
      • 4.2.2 Preliminaries
      • 4.2.3 Separability condition
      • 4.2.4 SeparabilityAnd reducibility
      • 4.2.5Applications
    • 4.3 ControllabilityAnd Observability of RLC Networks over F(z)
    • 4.4 Structural Condition of Controllability for RLC Networks over F(z)
      • 4.4.1 Separability conditions
      • 4.4.2 Structural controllability conditions
    • 4.5 Structural Condition of Observability for RLC Networks over F(z)
      • 4.5.1 Node voltage equationAnd two results
      • 4.5.2 Structural condition of observability over F(z)
    • 4.6 Separability, Reducibility, ControllabilityAnd Observability of RLCM Networks over F(z)
      • 4.6.1 Preliminaries
      • 4.6.2 Separability
      • 4.6.3 Reducibility
      • 4.6.4 ControllabilityAnd observability
      • 4.6.5 Structural condition of controllabilityAnd observability over F(z)
    • 4.7 Existence of State Equations of LinearActive Networks over F(z)
      • 4.7.1 Existence condition of state equation over F(z)
      • 4.7.2Application
    • 4.8A Sufficient Condition on ControllabilityAnd Observability ofActive Networks over F(z)
      • 4.8.1 Preliminaries
      • 4.8.2 Sufficient condition of controllability over F(z)
      • 4.8.3Applications
    • 4.9 Conditions on \overline B _ 11 \not =0And \widetilde C \not =0 ofActive Network over F(z)And Reducibility Condition of \overlineAAnd TheirApplications to ControllabilityAnd Observability
      • 4.9.1 Preliminaries
      • 4.9.2 Partitioning of \overline y And u_ 2 from u_1
      • 4.9.3 Conditions of \overline B _ 11 \not = 0
      • 4.9.4 Reducibility of \overline A And conditions of \widetilde C \neq0
      • 4.9.5 Examples
      • 4.9.6Applications to controllabilityAnd observability over F(z)
      • 4.9.7 Method of designingA structural controllableAnd observableActive network with normal form
    • 4.10 ComputerAssistantAnalysis Program for Networks over F(z)
      • 4.10.1 Software interface illumination
      • 4.10.2 StructuralAnalysis process description of the software
      • 4.10.3 Software functions
    • References
  • 5 Further Thought
    • 5.1 Independent Parameters--- The Third Type of Variables of Systems
    • 5.2 Physical Realization
      • 5.2.1 Canonical state space description of linear time-invariant systems
      • 5.2.2 Two basic properties
    • 5.3 Some Issues
      • 5.3.1 Is it irreducible when exist interaction?
      • 5.3.2 Dimension of nonzero mode \leqslant number of independent parameters
      • 5.3.3 Design ofActive networks being SC-SOAnd stable
    • 5.4 Quasi Structural ControllabilityAnd Observability Concept of Nonlinear SystemsAnd ItsApplications
      • 5.4.1 Preliminaries
      • 5.4.2 Quasi-structural controllability of nonlinear systems
      • 5.4.3Applications
      • 5.4.4 Conclusions
    • References
  • Appendix
    • AppendixA Some Well-known Results
      • A.1 Linear systems theory over R
      • A.2 Graph Theory
      • A.3 Linear graph
    • Appendix B Some Relevant Proofs in Theorem 4.11
      • B.1 The proof of \widehat C _ 12 \neq0
      • B.2 The proof of \widehat Y _ 12 \neq0
      • B.3 The proof of \widehat G _ 12 \neq0
      • B.4 The proof of \widehat L _ 12 \neq0 or \widehat Z _ 12 \neq0
    • Appendix C Proof of Theorem 4.15
    • Appendix D Proofs of some conclusions
      • D.1 The proof of Theorem 4.18
      • D.2 The proof of Theorem 4.19
      • D.3 Some results
    • References
  • Index
  • 版权

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