Stability of Linear Systems
Some Aspects of Kinematic Similarity
Published on 14. May 2014
247 pages
978-0-08-095661-9 (ISBN)
Description
Stability of Linear Systems: Some Aspects of Kinematic Similarity
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Series
Language
English
Place of publication
Oxford
United Kingdom
ISBN-13
978-0-08-095661-9 (9780080956619)
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11/1997
Academic Press
€68.09
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Content
- Front Cover
- Stability of Linear Systems: Some Aspects of Kinematic Similarity
- Copyright Page
- Preface
- Contents
- Chapter 1. Mathematical Preliminaries
- 1.1 Metric Spaces
- 1.2 Normed Metric Spaces
- 1.3 Contraction Mappings
- 1.4 Linear Operators
- 1.5 Linear Transformations and Matrices
- 1.6 Inner Product Spaces and Fourier Series
- 1.7 Notes
- References
- Chapter 2. Almost Periodic Functions
- 2.1 Introduction
- 2.2 Definitions and Elementary Properties of Almost Periodic Functions
- 2.3 Mean Values of Almost Periodic Functions and their Fourier Series
- 2.4 Almost Periodic Functions Depending Uniformly on a Parameter
- 2.5 Bochner's Criterion
- 2.6 Limiting Cases of Almost Periodic Functions
- 2.7 Notes
- References
- Chapter 3. Properties of Ordinary Differential Equations
- 3.1 Introduction
- 3.2 Existence and Uniqueness of Solution
- 3.3 Linear Ordinary Differential Equations
- 3.4 Constant Coefficient Differential Equations
- 3.5 Periodic Coefficients and Floquet Theory
- 3.6 Notes
- 3.7 References
- Chapter 4. Kinematic Similarity
- 4.1 Introduction
- 4.2 Liapunov Transformations and Kinematic Similarity
- 4.3 Invariants and Canonical Forms
- 4.4 Necessary and Sufficient Conditions for Kinematic Similarity
- 4.5 Estimates for Characteristic Exponents
- References
- Chapter 5. Stability Theory for Nonstationary Systems
- 5.1 Local Equilibrium Stability Conditions
- 5.2 Asymptotic Stability
- 5.3 Matrix Projections and Dichotomies of Linear Systems
- 5.4 Asymptotic Characteristic Value Stability Theory
- 5.5 Stability in the Large
- 5.6 Total Stability and Stability under Disturbances
- 5.7 Sufficient Conditions for Stability
- 5.8 Notes and Input-Output Stability
- References
- Chapter 6. Asymptotic Floquet Theory
- 6.1 Introduction
- 6.2 The Cappel-Bohr Lemma and Linear Differential Equations with Almost Periodic Coefficients
- 6.3 Coppel's Theorem
- 6.4 Almost Periodic Matrices Containing a Parameter
- References
- Chapter 7. Linear Systems with Variable Coefficients
- 7.1 Introduction and Survey of Applications
- 7.2 Beam Stabilisation in an Alternating Gradient Proton Synchrotron
- References
- Appendix 1. Existence of Solutions to Periodic and Almost Periodic Differential Systems
- Appendix 2. Dichotomies and Kinematic Similarity
- Appendix 3. Bibliography
- Subject Index
