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 |
Introduction / 1.: |
Nonlinear Differential Equations / 2.: |
Mathematical Preliminaries / 2.1: |