Differential Equations
Stability, Oscillations, Time Lags
Published on 14. May 2014
543 pages
978-0-08-095529-2 (ISBN)
Description
Differential Equations
More details
Series
Language
English
Place of publication
Oxford
United States
ISBN-13
978-0-08-095529-2 (9780080955292)
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Schweitzer Classification
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Additional editions
Aristide Halanay
Differential Equations
Book
03/1966
Academic Press
€81.84
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Content
- Front Cover
- Differential Equations: Stability, Oscillations, Time Lags
- Copyright Page
- Contents
- Preface to the English Edition
- Preface to the Rumanian Edition
- Introduction
- I.1 Vector Representation of Systems of Differential Equations
- I.2 The Existence Theorem
- I.3 Differential Inequalities
- I.4 The Uniqueness Theorem
- I.5 Theorems of Continuity and Differentiability with Respect to Initial Conditions
- Notes
- CHAPTER 1. Stability Theory
- 1.1 Theorems on Stability and Uniform Stability
- 1.2 Asymptotic Stability
- 1.3 Linear Systems
- 1.4 Stability for Linear Systems
- 1.5 Linear Systems with Constant Coefficients
- 1.6 The Lyapunov Function for Linear Systems with Constant Coefficients
- 1.7 Stability by the First Approximation
- 1.8 Total Stability
- 1.9 Linear Systems with Periodic Coefficients
- 1.10 The Perron Condition
- Notes
- CHAPTER 2. Absolute Stability of Nonlinear Control Systems
- 2.1 The Canonical Form and the Corresponding Lyapunov Function
- 2.2 Intrinsic Study of Control Systems
- 2.3 The Method of V . M . Popov
- 2.4 The Practical Stability of Systems with Elements of Relay Type
- Notes
- CHAPTER 3. Theory of Oscillations
- 3.1 Linear Oscillations
- 3.2 Almost-Periodic Solutions of Linear Systems
- 3.3 Quasi-Linear Systems
- 3.4 Systems Containing a Small Parameter
- 3.5 The Method of Averaging
- 3.6 Topological Methods
- 3.7 Autonomous Systems
- 3.8 Autonomous Systems Containing a Small Parameter
- 3.9 Periodic Solutions of the Second Kind
- 3.10 A Method of Successive Approximations
- 3.11 Periodic Perturbations of Autonomous Systems
- 3.12 Singular Perturbations
- Notes
- CHAPTER 4. Systems with Time Lag
- 4.1 The Existence Theorem . General Properties
- 4.2 Stability Theory
- 4.3 Linear Systems with Time Lag
- 4.4 The Perron Condition for Systems with Time Lag
- 4.5 An Estimate in the Stability Theory of Linear Systems with Time Lag
- 4.7 Periodic Linear Systems with Time Lag
- 4.8 Periodic Linear Systems with Time Lag. Stability Theory
- 4.9 Periodic Solutions of Linear Periodic Systems with Retarded Argument
- 4.10 The Critical Case for Linear Periodic Systems with Time Lag
- 4.11 Almost-Periodic Solutions for Linear Systems
- 4.12 Systems with a Small Parameter with Time Lag
- 4.13 Systems with Retarded Argument Containing a Small Parameter
- 4.14 Almost-Periodic Solutions for Quasi-Linear Systems with Time Lag
- 4.15 The Averaging Method for Systems with Retarded Argument
- 4.16 Other Theorems Relative to Periodic and Almost-Periodic Solutions of Systems with Time Lag
- 4.17 Singular Perturbation for Systems with Time Lag
- 4.18 Invariant Periodic Surfaces in a Class of Systems with Time Lag
- Notes
- Appendix
- A.1 Elements from the Theory of the Fourier Transform
- A.2 The Permutation of the Integration Order in Stieltjes' Integral
- Bibliography
- Subject Index
