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.

Description-Table Of Contents

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)[?]. 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). 2.5. Reducibility of square matrix over F(z). 2.6. Reducibility condition of class of matrices over F(z). 2.7. Two properties. 2.8. Independent parameters and a class of irreducible polynomials over F(z)[?]. 2.9. Conclusions. 2.10. New model and its reducibility -- 3. Controllability and observability of linear systems over F(z). 3.1. Controllability and observability in time domain. 3.2. Controllability and observability in frequency domain -- 4. Electrical networks over F(z). 4.1. Resistor-source networks over F(z). 4.2. Separability and reducibility conditions of RLC networks over F(z) and their applications. 4.3. Controllability and observability of RLC networks over F(z). 4.4. Structural condition of controllability for RLC networks over F(z). 4.5. Structural condition of observability for RLC networks over F(z). 4.6. Separability, reducibility, controllability and observability of RLCM networks over F(z). 4.7. Existence of state equations of linear active networks over F(z). 4.8. A sufficient condition on controllability and observability of active networks over F(z). 4.9. Conditions on [symbol] of active network over F(z) and reducibility condition of [symbol] and their applications to controllability and observability. 4.10. Computer assistant analysis program for networks over F(z) -- 5. Further thought. 5.1. Independent parameters - the third type of variables of systems. 5.2. Physical realization. 5.3. Some issues. 5.4. Quasi structural controllability and observability concept of nonlinear systems and its applications.