哈里尔编著的《非线性系统(第3版英文版)》是为研究生一年级的非线性系统或控制课程编写的，也可以作为工程技术人员或应用数学研究人员的参考书。它是作者在密歇根州立大学多年执教非线性系统课程的结晶。本书共十四章节，内容包括绪论、二阶系统、基本性质、李雅普诺夫稳定性、输入-输出稳定性、无源性、反馈系统的频域分析等。

本非线性系统的研究近年来受到越来越广泛的关注，国外许多工科院校已将“非线性系统”作为相关专业研究生的学位课程。哈里尔编著的《非线性系统(第3版英文版)》是美国密歇根州立大学电气与计算机工程专业的研究生教材，全书内容按照数学知识的由浅入深分成了四个部分。基本分析部分介绍了非线性系统的基本概念和基本分析方法；反馈系统分析部分介绍了输入-输出稳定性、无源性和反馈系统的频域分析；现代分析部分介绍了现代稳定性分析的基本概念、扰动系统的稳定性、扰动理论和平均化以及奇异扰动理论；非线性反馈控制部分介绍了反馈线性化，并给出了几种非线性设计工具，如滑模控制、李雅普诺夫再设计、反步设计法、基于无源性的控制和高增益观测器等。此外本书附录还汇集了一些书中用到的数学知识，包括基本数学知识的复习、压缩映射和一些较为复杂的定理证明。本书已根据作者于2012年4月2日更新过的勘误表进行过更正。

《非线性系统(第3版英文版)》既可以作为研究第一学期非线性系统课程的教材，也可以作为工程技术人员、应用数学专业人员的自学教材或参考书。

1 Introduction

1.1 Nonlinear Models and Nonlinear Phenomena

1.2 Examples

 1.2.1 Pendulum Equation

 1.2.2 Tunnel-Diode Circuit

 1.2.3 Mass-Spring System

 1.2.4 Negative-Resistance Oscillator

 1.2.5 Artificial Neural Network

 1.2.6 Adaptive Control

 1.2.7 Common Nonlinearities

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 Periodic Orbits

2.7 Bifurcation

2.8 Exercises

3 Fundamental Properties

3.1 Existence and Uniqueness

3.2 Continuous Dependence on Initial Conditions and Parameters

3.3 Differentiability of Solutions and Sensitivity Equations

3.4 Comparison Principle

3.5 Exercises

4 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 Feedback 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 kyapunov Stability

6.5 Feedback Systems: Passivity Theorems

6.6 Exercises

7 Frequency Domain Analysis of Feedback Systems

7.1 Absolute Stability

7.1.1 Circle Criterion

7.1.2 Popov Criterion

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 Periodic 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 Periodic Perturbation of Autonomous Systems

10.4 Averaging

10.5 Weakly Nonlinear Second-Order Oscillators

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 Stabilization via Linearization

12.3 Integral Control

12.4 Integral Control via Linearization

12.5 Gain Scheduling

12.6 Exercises

13 Feedback Linearization

13.1 Motivation

13.2 Input-Output kinearization

13.3 Full-State Linearization

13.4 State Feedback Control

13.4.1 Stabilization

13.4.2 Tracking

13.5 Exercises

14 Nonlinear Design Tools

14.1 Sliding Mode Control

 14.1.1 Motivating Example

 14.1.2 Stabilization

 14.1.3 Tracking

 14.1.4 Regulation via Integral Control

14.2 kyapunov Redesign

 14.2.1 Stabilization

 14.2.2 Nonlinear Damping

14.3 Backstepping

14.4 Passivity-Based Control

14.5 High-Gain Observers

 14.5.1 Motivating Example

 14.5.2 Stabilization

 14.5.3 Regulation via Integral Control

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 6.2

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