非线性系统（第三版 英文版）

Introduction.  
1.1 Nonlinear Models and Nonlinear Phenomena  
1.2 Examples  
1.3 Exercises  
2 Second-Order Systems  
2.1 Qualitative Behavior of Linear Systems  
2.2 Multiple Equilibria  
2.3 Qualitative Behavior Near Equilibrium Points  
2.4 Limit Cycles  
2.5 Numerical Construction of Phase Portraits  
2.6 Existence of Periodi Orbits  
2.7 Bifurcation  
2.8 Exercises  
3 Fundamental Properties  
3.1 Existen eand Uniqueness  
3.2 Continuous Dependence on Initial Conditions and Parameters  
3.3 Differentiability of Solutions and Sensitivity Equations  
3.4 Comparison Principle  
3.5 Exercises4 Lyapunov Stability  
4.1 Autonomous Systems  
4.2 The Invariance Principle  
4.3 Linear Systems and Linearization  
4.4 Comparison Functions  
4.5 Nonautonomous Systems  
4.6 Linear Time-Varying Systems and Linearization  
4.7 Converse Theorems  
4.8 Boundedness and Ultimate Boundedness  
4.9 Input-to-State Stability  
4.10 Exercises  
5 Input-Output Stability  
5.1 L Stability  
5.2 L Stability of State Models  
5.3 L2 Gain  
5.4 Feedba k Systems: The Small-Gain Theorem  
5.5 Exercises  
6 Passivity  
6.1 Memoryless Functions  
6.2 State Models  
6.3 Positive Real Transfer Functions  
6.4 L2 and Lyapunov Stability  
6.5 Feedback Systems: Passivity Theorems  
6.6 Exercises  
7 Frequency Domain Analysis of Feedback Systems  
7.1 Absolute Stability  
7.2 The Describing Function Method  
7.3 Exercises  
8 Advanced Stability Analysis  
8.1 The Center Manifold Theorem  
8.2 Region of Attraction  
8.3 Invariance-like Theorems  
8.4 Stability of Periodi Solutions  
8.5 Exercises  
9 Stability of Perturbed Systems  
9.1 Vanishing Perturbation  
9.2 Nonvanishing Perturbation  
9.3 Comparison Method  
9.4 Continuity of Solutions on the Infinite Interval  
9.5 Interconnected Systems..  
9.6 Slowly Varying Systems  
9.7 Exercises  
10 Perturbation Theory and Averaging  
10.1 The Perturbation Method  
10.2 Perturbation on the Infinite Interval  
10.3 Periodi Perturbation of Autonomous Systems  
10.4 Averaging  
10.5 Weakly Nonlinear Second-Order Os illators  
10.6 General Averaging  
10.7 Exercises  
11 Singular Perturbations  
11.1 The Standard Singular Perturbation Model  
11.2 Time-Scale Properties of the Standard Model  
11.3 Singular Perturbation on the Infinite Interval  
11.4 Slow and Fast Manifolds  
11.5 Stability Analysis  
11.6 Exercises  
12 Feedback Control  
12.1 Control Problems  
12.2 Stabilizationcvia Linearization  
12.3 Integral Control  
12.4 Integral Controlcvia Linearization  
12.5 Gain Scheduling  
12.6 Exercises  
13 Feedback Linearization  
13.1 Motivation  
13.2 Input-Output Linearization  
13.3 Full-State Linearization  
13.4 State Feedback Control  
13.5 Exercises  
14 Nonlinear Design Tools  
14.1 Sliding Mode Control  
14.2 kyapunov Redesign  
14.3 Backstepping  
14.4 Passivity-Based Control  
14.5 High-Gain Observers  
14.6 Exercises  
A Mathematical Review  
B Contraction Mapping  
C Proofs  
C.1 Proof of Theorems 3.1 and 3.2  
C.2 Proof of Lemma 3.4  
C.3 Proof of Lemma 4.1  
C.4 Proof of Lemma 4.3  
C.5 Proof of Lemma 4.4  
C.6 Proof of Lemma 4.5  
C.7 Proof of Theorem 4.16  
C.8 Proof of Theorem 4.17  
C.9 Proof of Theorem 4.18  
C.10 Proof of Theorem 5.4  
C.11 Proof of Lemma 6.1  
C.12 Proof of Lemma 612  
C.13 Proof of Lemma 7.1  
C.14 Proof of Theorem 7.4  
C.15 Proof of Theorems 8.1 and 8.3  
C.16 Proof of Lemma 8.1  
C.17 Proof of Theorem 11.1  
C.18 Proof of Theorem 11.2  
C.19 Proof of Theorem 12.1  
C.20 Proof of Theorem 12.2  
C.21 Proof of Theorem 13.1  
C.22 Proof of Theorem 13.2  
C.23 Proof of Theorem 14.6  
Note and References  
Bibliography  
Symbols  
Index...