General systems theory mathematical foundations
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrang...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | eBook |
| Language: | English |
| Published: |
New York
Academic Press
1975, 1975
|
| Series: | Mathematics in science and engineering
|
| Subjects: | |
| Online Access: | |
| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
Table of Contents:
- Includes bibliographical references and index
- Chapter X. Interconnections of Subsystems, Decomposition, and Decoupling
- 1. Connecting Operators
- 2. Subsystems, Components, and Decomposition
- 3. Feedback Connection of Components
- 4. Decoupling and Functional Controllability
- 5. Abstract Pole Assignability
- 6. Simplification through Decomposition of Discrete-Time Dynamical Systems
- Chapter XI. Computability, Consistency, and Completeness
- 1. Computation as Dynamical Process
- 2. Fundamental Diagonalization (Goedel) Theorem
- 3. Application of the Fundamental Theorem to Formal Systems
- 4. Realization by Turing Machines
- Chapter XII. Categories of Systems and Associated Functors
- 1. Formation of Categories of General Systems and Homomorphic Models
- 2. Categories of General Systems
- 3. Categories of Time Systems
- 4. Categories of Dynamical Systems
- Appendix I. References and Historical Account
- Appendix II. Alternative Basis for Mathematical General Systems Theory
- 1. Axiomatic Logic Structures
- 2. Topological. Functional Analysis, and Quantitative Approaches
- 3. Algebraic Systems Theory
- 4. Restricted Notion of a System
- Appendix III. Open Systems and Goal-Seeking Systems
- 1. Open Systems
- 2. Goal-Seeking Systems
- Appendix IV. Basic Notions in Category Theory
- Index
- Cover13;
- General Systems Theory: Mathematical Foundations
- Copyright Page
- Contents
- Preface
- Chapter I. Introduction
- 1. General Systems Theory: What Is It and What Is It for?
- 2. Formalization Approach for the Development of the Mathematical Theory of General Systems
- Chapter II. Basic Concepts
- 1. Set-Theoretic Concept of a General System
- 2. General Time and Dynamical Systems
- 3. Auxiliary Functions and Some Basic Classification of Systems
- 4. Causality
- Chapter III. General Realization Theory
- 1. Realizability and Dynamical Representation
- 2. Canonical Representation (Decomposition) of Dynamical Systems and Characterization of States
- 3. Constructive Origin of State-Space Representation
- Chapter IV. Linearity
- 1. Linear Time Systems
- 2. Decomposition of Systems Response: State- and Input-Response Functions
- 3. Realization Theory
- 4. Construction of the State Space for a Linear System
- Chapter V. Past-Determinacy
- 1. On the Class of Past-Determined Systems
- 2. State-Space Representation
- 3. Characterization of Past-Determined Systems
- Chapter VI. Stationarity and Time Invariance
- 1. State-Space Stationarity and Time Invariance
- 2. Realization Theory of Time-Invariant Systems
- 3. Stationary Past-Determined Systems
- 4. Axiomatic Construction of a Class of Dynamical Systems
- 5. Abstract Transfer Function
- Chapter VII. Controllability
- 1. Basic Concepts
- 2. Some General Conditions for Controllability
- 3. Controllability of Time Systems
- 4. Overview of Some Basic Linear Time Systems Properties Related to Controllability
- Chapter VIII. Minimal Realization
- 1. Concepts of Minimal Realizations
- 2. Characterization of the Minimal Realization of Stationary Systems
- 3. Uniqueness of Minimal Input-Response Realization
- Chapter IX. Stability
- 1. General Concept of Stability
- 2. Stability of Sets for General Systems