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"Lu, Kai-Sheng"
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Rational function systems and electrical networks with multi-parameters
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.
eBook
Electrical Networks over F(z)
The following sections are included:
Resistor-Source Networks over F(z)
Introduction
General resistor-source networks
Unhinged networks
Effects of single source
Separability and Reducibility Conditions of RLC Networks over F(z) and Their Applications
Introduction
Preliminaries
Separability condition
Separability and reducibility
Applications
Controllability and Observability of RLC Networks over F(z)
Structural Condition of Controllability for RLC Networks over F(z)
Separability conditions
Structural controllability conditions
Structural Condition of Observability for RLC Networks over F(z)
Node voltage equation and two results
Structural condition of observability over F(z)
Separability, Reducibility, Controllability and Observability of RLCM Networks over F(z)
Preliminaries
Separability
Reducibility
Controllability and observability
Structural condition of controllability and observability over F(z)
Existence of State Equations of Linear Active Networks over F(z)
Existence condition of state equation over F(z)
Application
A Sufficient Condition on Controllability and Observability of Active Networks over F(z)
Preliminaries
Sufficient condition of controllability over F(z)
Applications
Conditions on $\\overline{B}_{11} \\neq 0$ and $\\tilde{C} \\neq 0$ of Active Network over F(z) and Reducibility Condition of Ā and Their Applications to Controllability and Observability
Preliminaries
Partitioning of ȳ and u2 from u1
Conditions of $\\overline{B}_{11} \\neq 0$
Reducibility of Ā and conditions of $\\tilde{C} \\neq 0$
Examples
Applications to controllability and observability over F(z)
Method of designing a structural controllable and observable active network with normal form
Computer Assistant Analysis Program for Networks over F(z)
Software interface illumination
Structural analysis process description of the software
Software functions
References
Book Chapter
Matrices over Field F(z) of Rational Functions in Multi-parameters
The following sections are included:
Polynomials over Field F(z) or Ring F(z)[⋋]
Operations and Determinant of Matrix over F(z)
Elementary Operations of Matrices over F(z) and Some Conclusions
Operation and Canonical Form of Matrix over F(z)
Matrix over F(z) and its canonical expression
Characteristic matrix
Two canonical forms of nonderogatory matrix
Rational canonical form and general Jordan canonical form
Reducibility of Square Matrix over F(z)
Reducibility Condition of Class of Matrices over F(z)
A class of RFM
Some lemmas and definitions
Reducibility condition
Applications
Summary
Two Properties
Some lemmas
Type-1 matrix has two properties
Problems
Independent Parameters and a Class of Irreducible Polynomials over F(z)[⋋]
Conclusions
New Model and Its Reducibility
The new model
Reducibility condition
References
Book Chapter
Controllability and Observability of Linear Systems over F(z)
The following sections are included:
Controllability and Observability in Time Domain
Preliminaries [Lu, 2001]
Controllability criteria [Lu, 2001]
The canonical decomposition of controllability and observability of systems
Criterions to linear physical systems
Applications to control systems
Controllability and Observability in Frequency Domain
General systems [Lu et al., 1991]
SC-SO of composite systems [Lu et al., 1991]
Polynomial matrix➁[Liu, 2008]
References
Book Chapter
Further Thought
The following sections are included:
Independent Parameters — The Third Type of Variables of Systems
Physical Realization
Canonical state space description of linear time-invariant systems
Two basic properties
Some Issues
Is it irreducible when exist interaction?
Dimension of nonzero mode $\\leqslant$ number of independent parameters
Design of active networks being SC-SO and stable
Quasi Structural Controllability and Observability Concept of Nonlinear Systems and Its Applications
Preliminaries
Quasi-structural controllability of nonlinear systems
Applications
Conclusions
References
Book Chapter