UID:
almahu_9947366453702882
Umfang:
1 online resource (543 p.)
ISBN:
1-282-28917-9
,
9786612289170
,
0-08-095529-0
Serie:
Mathematics in science and engineering ; 23
Inhalt:
Differential equations; stability, oscillations, time lags
Anmerkung:
Translation of Teoria calitativa a ecuatiilor diferentiale.
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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
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1.5 Linear Systems with Constant Coefficients1.6 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
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3.2 Almost-Periodic Solutions of Linear Systems3.3 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
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4.4 The Perron Condition for Systems with Time Lag4.5 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
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4.14 Almost-Periodic Solutions for Quasi-Linear Systems with Time Lag4.15 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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English
Weitere Ausg.:
ISBN 0-12-317950-5
Sprache:
Englisch
