| Preface | p. v |
| Acknowledgments | p. vii |
| Introduction | p. 1 |
| References | p. 8 |
| Matrices over Field F(z) of Rational Functions in Multi-parameters | p. 11 |
| Polynomials over Field F(z) or Ring F(z)[] | p. 11 |
| Operations and Determinant of Matrix over F(z) | p. 12 |
| Elementary Operations of Matrices over F(z) and Some Conclusions | p. 12 |
| Operation and Canonical Form of Matrix over F(z) | p. 14 |
| Matrix over F(z) and its canonical expression | p. 14 |
| Characteristic matrix | p. 23 |
| Two canonical forms of nonderogatory matrix | p. 27 |
| Rational canonical form and general Jordan canonical form | p. 32 |
| Reducibility of Square Matrix over F(z) | p. 35 |
| Reducibility Condition of Class of Matrices over F(z) | p. 36 |
| A class of RFM | p. 36 |
| Some lemmas and definitions | p. 36 |
| Reducibility condition | p. 39 |
| Applications | p. 48 |
| Summary | p. 51 |
| Two Properties | p. 51 |
| Some lemmas | p. 52 |
| Type-1 matrix has two properties | p. 54 |
| Problems | p. 59 |
| Independent Parameters and a Class of Irreducible Polynomials over F(z)[] | p. 59 |
| Conclusions | p. 64 |
| New Model and Its Reducibility | p. 68 |
| The new model | p. 68 |
| Reducibility condition | p. 69 |
| References | p. 71 |
| Controllability and Observability of Linear Systems over F(z) | p. 73 |
| Controllability and Observability in Time Domain | p. 73 |
| Preliminaries [Lu, 2001] | p. 73 |
| Controllability criteria [Lu, 2001] | p. 75 |
| The canonical decomposition of controllability and observability of systems | p. 87 |
| Criterions to linear physical systems | p. 89 |
| Applications to control systems | p. 100 |
| Controllability and Observability in Frequency Domain | p. 102 |
| General systems [Lu et al., 1991] | p. 102 |
| SC-SO of composite systems [Lu et al., 1991] | p. 106 |
| Polynomial matrix [Liu, 2008] | p. 113 |
| References | p. 120 |
| Electrical Networks over F(z) | p. 121 |
| Resistor-Source Networks over F(z) | p. 121 |
| Introduction | p. 121 |
| General resistor-source networks | p. 123 |
| Unhinged networks | p. 131 |
| Effects of single source | p. 135 |
| Separability and Reducibility Conditions of RLC Networks over F(z) and Their Applications | p. 140 |
| Introduction | p. 140 |
| Preliminaries | p. 141 |
| Separability condition | p. 143 |
| Separability and reducibility | p. 146 |
| Applications | p. 147 |
| Controllability and Observability of RLC Networks over F(z) | p. 149 |
| Structural Condition of Controllability for RLC Networks over F(z) | p. 151 |
| Separability conditions | p. 151 |
| Structural controllability conditions | p. 154 |
| Structural Condition of Observability for RLC Networks over F(z) | p. 155 |
| Node voltage equation and two results | p. 156 |
| Structural condition of observability over F(z) | p. 158 |
| Separability, Reducibility, Controllability and Observability of RLCM Networks over F(z) | p. 160 |
| Preliminaries | p. 160 |
| Separability | p. 161 |
| Reducibility | p. 166 |
| Controllability and observability | p. 168 |
| Structural condition of controllability and observability over F(z) | p. 173 |
| Existence of State Equations of Linear Active Networks over F(z) | p. 177 |
| Existence condition of state equation over F(z) | p. 177 |
| Application | p. 181 |
| A Sufficient Condition on Controllability and Observability of Active Networks over F(z) | p. 185 |
| Preliminaries | p. 186 |
| Sufficient condition of controllability over F(z) | p. 189 |
| Applications | p. 189 |
| Conditions on B11 ≠ 0 and C ≠ 0 of Active Network over F(z) and Reducibility Condition of A and Their Applications to Controllability and Observability | p. 190 |
| Preliminaries | p. 191 |
| Partitioning of y and u2 from u1 | p. 193 |
| Conditions of B11 ≠ 0 | p. 198 |
| Reducibility of A and conditions of C ≠ 0 | p. 203 |
| Examples | p. 207 |
| Applications to controllability and observability over F(z) | p. 213 |
| Method of designing a structural controllable and observable active network with normal form | p. 223 |
| Computer Assistant Analysis Program for Networks over F(z) | p. 224 |
| Software interface illumination | p. 224 |
| Structural analysis process description of the software | p. 226 |
| Software functions | p. 232 |
| References | p. 235 |
| Further Thought | p. 237 |
| Independent Parameters - The Third Type of Variables of Systems | p. 237 |
| Physical Realization | p. 238 |
| Canonical state space description of linear time-invariant systems | p. 238 |
| Two basic properties | p. 239 |
| Some Issues | p. 240 |
| Is it irreducible when exist interaction? | p. 241 |
| Dimension of nonzero mode ≤ number of independent parameters | p. 242 |
| Design of active networks being SC-SO and stable | p. 242 |
| Quasi Structural Controllability and Observability Concept of Nonlinear Systems and Its Applications | p. 243 |
| Preliminaries | p. 243 |
| Quasi-structural controllability of nonlinear systems | p. 245 |
| Applications | p. 246 |
| Conclusions | p. 249 |
| References | p. 249 |
| Appendix | p. 251 |
| Some Well-known Results | p. 251 |
| Linear systems theory over R | p. 251 |
| Controllability criterions in time domain | p. 251 |
| Polynomial matrix theory in frequency domain | p. 253 |
| Graph theory | p. 258 |
| Linear graph | p. 262 |
| Linear graph | p. 262 |
| Relationships in RLC networks | p. 272 |
| Some Relevant Proofs in Theorem 4.11 | p. 274 |
| The proof of C12 ≠ 0 | p. 274 |
| The proof of Y12 ≠ 0 | p. 275 |
| The proof of G12 ≠ 0 | p. 277 |
| The proof of L12 ≠ 0 or Z12 ≠ 0 | p. 279 |
| Proof of Theorem 4.15 | p. 282 |
| Proofs of some conclusions | p. 287 |
| The proof of Theorem 4.18 | p. 287 |
| The proof of Theorem 4.19 | p. 293 |
| Some results | p. 297 |
| References | p. 302 |
| Index | p. 303 |
| Table of Contents provided by Ingram. All Rights Reserved. |
