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
