多元有理函数系统与电网络 英文版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

多元有理函数系统与电网络 英文版PDF格式电子书版下载

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1 Introduction1

References8

2 Matrices over Field F(z)of Rational Functions in Multi-parameters11

2.1 Polynomials over Field F(z)or Ring F(z)[λ]11

2.2 Operations and Determinant of Matrix over F(z)12

2.3 Elementary Operations of Matrices over F(z)and Some Conclusions12

2.4 Operation and Canonical Form of Matrix over F(z)14

2.4.1 Matrix over F(z)and its canonical expression14

2.4.2 Characteristic matrix23

2.4.3 Two canonical forms of nonderogatory matrix27

2.4.4 Rational canonical form and general Jordan canonical form32

2.5 Reducibility of Square Matrix over F(z)35

2.6 Reducibility Condition of Class of Matrices over F(z)36

2.6.1 A class of RFM36

2.6.2 Some lemmas and definitions36

2.6.3 Reducibility condition39

2.6.4 Applications48

2.6.5 Summary51

2.7 Two Properties51

2.7.1 Some lemmas52

2.7.2 Type-1 matrix has two properties54

2.7.3 Problems59

2.8 Independent Parameters and a Class of Irreducible Polynomials over F(z)[λ]59

2.9 Conclusions64

2.10 New Model and Its Reducibility68

2.10.1 The new model68

2.10.2 Reducibility condition69

References71

3 Controllability and Observability of Linear Systems over F(z)73

3.1 Controllability and Observability in Time Domain73

3.1.1 Preliminaries [Lu,2001]73

3.1.2 Controllability criteria[Lu,2001]75

3.1.3 The canonical decomposition of controllability and observability of systems87

3.1.4 Criterions to linear physical systems89

3.1.5 Applications to control systems100

3.2 Controllability and Observability in Frequency Domain102

3.2.1 General systems[Lu et al.,1991]102

3.2.2 SC-SO of composite systems[Lu et al.,1991]106

3.2.3 Polynomial matrix [Liu,2008]113

References120

4 Electrical Networks over F(z)121

4.1 Resistor-Source Networks over F(z)121

4.1.1 Introduction121

4.1.2 General resistor-source networks123

4.1.3 Unhinged networks131

4.1.4 Effects of single source135

4.2 Separability and Reducibility Conditions of RLC Networks over F(z)and Their Applications140

4.2.1 Introduction140

4.2.2 Preliminaries141

4.2.3 Separability condition143

4.2.4 Separability and reducibility146

4.2.5 Applications147

4.3 Controllability and Observability of RLC Networks over F(z)149

4.4 Structural Condition of Controllability for RLC Networks over F(z)151

4.4.1 Separability conditions151

4.4.2 Structural controllability conditions154

4.5 Structural Condition of Observability for RLC Networks over F(z)155

4.5.1 Node voltage equation and two results156

4.5.2 Structural condition of observability over F(z)158

4.6 Separability,Reducibility,Controllability and Observability of RLCM Networks over F(z)160

4.6.1 Preliminaries160

4.6.2 Separability161

4.6.3 Reducibility166

4.6.4 Controllability and observability168

4.6.5 Structural condition of controllability and observability over F(z)173

4.7 Existence of State Equations of Linear Active Networks over F(z)177

4.7.1 Existence condition of state equation over F(z)177

4.7.2 Application181

4.8 A Sufficient Condition on Controllability and Observability of Active Networks over F(z)185

4.8.1 Preliminaries186

4.8.2 Sufficient condition of controllability over F(z)189

4.8.3 Applications189

4.9 Conditions on ？11≠0 and ？≠0 of Active Network over F(z)and Reducibility Condition of ？ and Their Applications to Controllability and Observability190

4.9.1 Preliminaries191

4.9.2 Partitioning of？and u2 from u1193

4.9.3 Conditions of ？11≠0198

4.9.4 Reducibility of ？ and conditions of ？≠0203

4.9.5 Examples207

4.9.6 Applications to controllability and observability over F(z)213

4.9.7 Method of designing a structural controllable and observable active network with normal form223

4.10 Computer Assistant Analysis Program for Networks over F(z)224

4.10.1 Software interface illumination224

4.10.2 Structural analysis process description of the software226

4.10.3 Software functions232

References235

5 Further Thought237

5.1 Independent Parameters—The Third Type of Variables of Systems237

5.2 Physical Realization238

5.2.1 Canonical state space description of linear time-invariant systems238

5.2.2 Two basic properties239

5.3 Some Issues240

5.3.1 Is it irreducible when exist interaction?241

5.3.2 Dimension of nonzero mode≤number of independent parameters242

5.3.3 Design of active networks being SC-SO and stable242

5.4 Quasi Structural Controllability and Observability Concept of Nonlinear Systems and Its Applications243

5.4.1 Preliminaries243

5.4.2 Quasi-structural controllability of nonlinear systems245

5.4.3 Applications246

5.4.4 Conclusions249

References249

Appendix251

Appendix A Some Well-known Results251

A.1 Linear systems theory over R251

A.1.1 Controllability criterions in time domain251

A.1.2 Polynomial matrix theory in frequency domain253

A.2 Graph theory258

A.3 Linear graph262

A.3.1 Linear graph262

A.3.2 Relationships in RLC networks272

Appendix B Some Relevant Proofs in Theorem 4.11274

B.1 The proof of ？12≠0274

B.2 The proof of ？12≠0275

B.3 The proof of ？12≠0277

B.4 The proof of ？12≠0 or ？12≠0279

Appendix C Proof of Theorem 4.15282

Appendix D Proofs of some conclusions287

D.1 The proof of Theorem 4.18287

D.2 The proof of Theorem 4.19293

D.3 Some results297

References302

Index303