多元有理函數系統與電網絡（簡體書）

《多元有理函數系統與電網絡（英文版）》主要介紹多元有理函數系統與電網絡的結構和性質，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量代換條件，域F（z）上線性系統的結構能控能觀性問題、電網絡的結構性質、RLCM網絡的可斷性和可約性及能控能觀性、有源網絡狀態方程的存在性條件、能控能觀性條件等；附錄給出了《多元有理函數系統與電網絡（英文版）》用到的一些知識。
《多元有理函數系統與電網絡（英文版）》適合電子電氣、自動化和應用數學（矩陣理論）專業的研究生、科研和工程技術人員參考閱讀。．

《多元有理函數系統與電網絡(英文版)》主要以英文版的形式介紹了關于多元化的有理函數系統以及電網絡的知識，同時也用到了關于數學函數，線性系統，狀態方程，RLCM網絡等知識。《多元有理函數系統與電網絡(英文版)》適合電子電氣、自動化和應用數學（矩陣理論）專業的研究生、科研和工程技術人員參考閱讀。

Preface
Acknowledgments
1Introduction
References

2MatricesoverFieldF（z）ofRationalFunctionsinMulti-parameters
2.1PolynomialsoverFieldF（z）orRingF（z）[隴
2.2OperationsandDeterminantofMatrixoverF（z）
2.3ElementaryOperationsofMatricesoverF（z）andSomeConclusions
2.4OperationandCanonicalFormofMatrixoverF（z）
2.4.1MatrixoverF（z）anditscanonicalexpression
2.4.2Characteristicmatrix
2.4.3Twocanonicalformsofnonderogatorymatrix
2.4.4RationalcanonicalformandgeneralJordancanonicalform
2.5ReducibilityofSquareMatrixoverF（z）
2.6ReducibilityConditionofClassofMatricesoverF（z）
2.6.1AclassofRFM
2.6.2Somelemmasanddefinitions
2.6.3Reducibilitycondition
2.6.4Applications
2.6.5Summary
2.7TwoProperties
2.7.1Somelemmas
2.7.2Type-lmatrixhastwoproperties
2.7.3Problems
2.8IndependentParametersandaClassoflrreduciblePolynomialsoverF（z）[隴
2.9Conclusions
2.10NewModelandItsReducibility
2.10.1Thenewmodel
2.10.2Reducibilitycondition
References

3ControllabilityandObservabilityofLinearSystemsoverF（z）
3.1ControllabilityandObservabilityinTimeDomain
3.1.1Preliminaries[Lu，2001]
3.1.2Controllabilitycriteria[Lu，2001]
3.1.3Thecanonicaldecompositionofcontrollabilityandobservabilityofsystems
3.1.4Criterionstolinearphysicalsystems
3.1.5Applicationstocontrolsystems
3.2ControllabilityandObservabilityinFrequencyDomain
3.2.1Generalsystems[Luetal.，1991]
3.2.2SC-SOofcompositesystems[Luetal.，1991]
3.2.3Polynomialmatrix[Liu，2008]References

4ElectricalNetworksoverF（z）
4.1Resistor-SourceNetworksoverF（z）
4.1.1Introduction
4.1.2Generalresistor-sourcenetworks
4.1.3Unhingednetworks
4.1.4Effectsofsinglesource
4.2SeparabilityandReducibilityConditionsofRLCNetworksoverF（z）andTheirApplications
4.2.1Introduction
4.2.2Preliminaries
4.2.3Separabilitycondition
4.2.4Separabilityandreducibility
4.2.5Applications
4.3ControllabilityandObservabilityofRLCNetworksoverF（z）

5FurtherThought
Appendix
Index．

At present,the main function of the software includes two aspects: drawing schematic and analysis of electrical network,and the electrical network analysis is the main function of the software.
As a general classification,electrical networks can be divided into active networks and passive networks.For passive networks,software analysis functions include to initiate inspection of network,to number the nodes in networks,to choose twigs and links in networks,and to count the number of connected graphs in networks(i.e.,the number of trees contained in networks),the state equations of networks(including the state equation and output equation),the complexity of networks,the rank of the coefficient matrix A,the rank of the controllability matrix Tc and structural controllability and observability of networks.The initial examination is to check that whether the network has component short circuited,all-voltage source loops,or all-current source cut-sets first.The program gives a warning and hint user to modify circuit for these cases; the number of trees in network means the number of connected graphs.
The analysis of the active network is similar to that of passive networks.However,it is not perfect.The main functions are currently: to initiate inspection of network,to number the nodes in networks,to choose twigs and links in networks,and to count the number of connected graphs in networks,the state equations of networks,the complexity of networks,the rank of the coefficient matrix A.Besides that mentioned in the case of passive networks,network initial inspection still include checking whether the network has allvoltage source loops including controlled voltage source,all-current source cut-sets including controlled current source.The programs will give a warning for these two cases.