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Preface to the Classics Edition

Preface

Note to the Reader

Introduction / 1.：

Nonlinear Differential Equations / 2.：

Mathematical Preliminaries / 2.1：

Induced Norms and Matrix Measures / 2.2：

Contraction Mapping Theorem / 2.3：

Solution Estimates / 2.4：

Second-Order Systems / 3.：

Preliminaries / 3.1：

Linearization Method / 3.2：

Periodic Solutions / 3.3：

Two Analytical Approximation Methods / 3.4：

Approximate Analysis Methods / 4.：

Describing Functions / 4.1：

Periodic Solutions: Rigorous Arguments / 4.2：

Singular Perturbations / 4.3：

Lyapunov Stability / 5.：

Stability Definitions / 5.1：

Some Preliminaries / 5.2：

Lyapunov's Direct Method / 5.3：

Stability of Linear Systems / 5.4：

Lyapunov's Linearization Method / 5.5：

The Lur'e Problem / 5.6：

Converse Theorems / 5.7：

Applications of Converse Theorems / 5.8：

Discrete-Time Systems / 5.9：

Input-Output Stability / 6.：

L[subscript p]-Spaces and their Extensions / 6.1：

Definitions of Input-Output Stability / 6.2：

Relationships Between I/O and Lyapunov Stability / 6.3：

Open-Loop Stability of Linear Systems / 6.4：

Linear Time-Invariant Feedback Systems / 6.5：

Time-Varying and/or Nonlinear Systems / 6.6：

Differential Geometric Methods / 6.7：

Basics of Differential Geometry / 7.1：

Distributions, Frobenius Theorem / 7.2：

Reachability and Observability / 7.3：

Feedback Linearization: Single-Input Case / 7.4：

Feedback Linearization: Multi-Input Case / 7.5：

Input-Output Linearization / 7.6：

Stabilization of Linearizable Systems / 7.7：

Prevalence of Differential Equations with Unique Solutions / A.：

Proof of the Kalman-Yacubovitch Lemma / B.：

Proof of the Frobenius Theorem / C.：

References

Index

Preface to the Classics Edition

Preface

Note to the Reader

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Representation of Physical Quantities by Mathematical Functions

Special Functions

Harmonic Analysis

Mathematical Operators and Physical Systems

Convolution

The Fourier Transform

Characteristics and Applications of Linear Filters

Two-Dimensional Convolution and Fourier Transformation

The Propagation and Diffraction of Optical Wave Fields

Image-Forming Systems

Appendices

Index

Representation of Physical Quantities by Mathematical Functions

Special Functions

Harmonic Analysis

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