Differential Equations

Name: Differential Equations | Stability, Oscillations, Time Lags
Brand: Academic Press
Price: 88.95 EUR
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Stability, Oscillations, Time Lags

Halanay(Autor*in)

Halanay(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

543 Seiten

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978-0-08-095529-2 (ISBN)

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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

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