Rational function systems and electrical networks with multi-parameters / Kai-Sheng Lu.

Format:

Book

Author/Creator:

Lu, Kai-Sheng.

Language:

English

Subjects (All):

Electric circuits.

Electric networks.

Matrices.

Physical Description:

1 online resource (319 p.)

Edition:

1st ed.

Place of Publication:

New Jersey : World Scientific, c2012.

Language Note:

English

Summary:

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 ); separabi

Contents:

Preface; Acknowledgments; Contents; References; 1 Introduction; 2 Matrices over Field F(z) of Rational Functions in Multi-parameters; 2.1 Polynomials over Field F(z) or Ring F(z)[λ]; 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-1 matrix has two properties; 2.7.3 Problems; 2.8 Independent Parameters and a Class of Irreducible Polynomials over F(z)[λ]; 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 Networks over F(z); 4.4 Structural Condition of Controllability for RLC Networks over F(z); 4.4.1 Separability conditions; 4.4.2 Structural controllability conditions; 4.5 Structural Condition of Observability for RLC Networks over F(z)

4.5.1 Node voltage equation and two results 4.5.2 Structural condition of observability over F(z); 4.6 Separability, Reducibility, Controllability and Observability of RLCM Networks over F(z); 4.6.1 Preliminaries; 4.6.2 Separability; 4.6.3 Reducibility; 4.6.4 Controllability and observability; 4.6.5 Structural condition of controllability and observability over F(z); 4.7 Existence of State Equations of Linear Active Networks over F(z); 4.7.1 Existence condition of state equation over F(z); 4.7.2 Application

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

981-4412-43-0

OCLC:

841206456