Qualitative Analysis of Large Scale Dynamical Systems
Published on 14. May 2014
307 pages
978-0-08-095643-5 (ISBN)
Description
This book develops a unified approach to qualitative analysis of large scale systems described by many diversified types of equations.
More details
Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095643-5 (9780080956435)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Anthony N. Michel | Richard K. Miller
Qualitative Analysis of Large Scale Dynamical Systems
Book
01/1977
Academic Press
€66.85
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Content
- Front Cover
- Qualitative Analysis of Large Scale Dynamical Systems
- Copyright Page
- Contents
- Preface
- Acknowledgments
- Chapter I. Introduction
- 1.1 Introduction
- 1.2 Qualitative Analysis of Dynarnical Systems: General Remarks
- 1.3 Qualitative Analysis of Large Scale Systems: General Remarks
- 1.4 An Overview of the Subsequent Chapters
- Chapter II. Systems Described by Ordinary Differential Equations
- 2.1 Notation
- 2.2 Lyapunov Stability and Related Results
- 2.3 Large Scale Systems
- 2.4 Analysis by Scalar Lyapunov Functions
- 2.5 Application of M-Matrices
- 2.6 Application of the Comparison Principle to Vector Lyapunov Functions
- 2.7 Estimates of Trajectory Behavior and Trajectory Bounds
- 2.8 Applications
- 2.9 Notes and References
- Chapter III. Discrete Time Systems and Sampled Data Systems
- 3.1 Systems Described by Difference Equations
- 3.2 Large Scale Systems
- 3.3 Stability and Instability of Large Scale Systems
- 3.4 Examples
- 3.5 Sampled Data Systems
- 3.6 Notes and References
- Chapter IV. Systems Described by Stochastic Differential Equations
- 4.1 Notation
- 4.2 Systems Described by Stochastic Differential Equations
- 4.3 Composite Systems
- 4.4 Analysis by Scalar Lyapunov Functions
- 4.5 Analysis by Vector Lyapunov Functions
- 4.6 Examples
- 4.7 Notes and References
- Chapter V. Infinite-Dimensional Systems
- 5.1 Notation
- 5.2 Co-Semigroups
- 5.3 Nonlinear Semigroups
- 5.4 Lyapunov Stability of Dynamical Systems
- 5.5 Examples of Semigroups
- 5.6 Stability of Large Scale Systems Described on Banach Spaces
- 5.7 Some Examples and Applications
- 5.8 Functional Differential Equations-Special Results
- 5.9 Application of Comparison Theorems to Vector Lyapunov Functions
- 5.10 Notes and References
- Chapter VI. Input-Output Stability of Large Scale Systems
- 6.1 Preliminaries
- 6.2 Stability of Large Scale Systems: Results Involving Gains
- 6.3 Instability of Large Scale Systems
- 6.4 Stability of Large Scale Systems: Results Involving Sector and Conicity Conditions
- 6.5 Stability of Large Scale Systems: Popov-Like Conditions
- 6.6 L8-Stability and l8-Stability of Large Scale Systems
- 6.7 Analysis and Design Procedure
- 6.8 Notes and References
- Chapter VII. Integrodifferential Systems
- 7.1 Preliminary Results
- 7.2 L2-Stability and Instability of Interconnected Systems
- 7.3 Linear Equations and Linearized Equations
- 7.4 An Example
- 7.5 Notes and References
- References
- Index
