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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Mesarovi�c, Mihajlo D.
Otros Autores: Takahara, Yasuhiko, 1935-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York : Academic Press, 1975.
Colección:Mathematics in science and engineering ; v. 113.
Temas:
System analysis.
Analyse de syst�emes.
systems analysis.
SCIENCE > System Theory.
TECHNOLOGY & ENGINEERING > Operations Research.
System analysis
Grundlage
Systemtheorie
Mathematik
SYSTEMS ANALYSIS.
General systems theory
Acceso en línea:Texto completo
Texto completo
Texto completo
Tabla de Contenidos:
  • 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
  • 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.

Ejemplares similares