非線性系統的研究近年來受到越來越廣泛的關注，國外許多工科院校已將"非線性系統”作為相關專業研究生的學位課程。本書是美國密歇根州立大學電氣與計算機工程專業的研究生教材，全書內容按照數學知識的由淺入深分成了四個部分。基本分析部分介紹了非線性系統的基本概念和基本分析方法；反饋系統分析部分介紹了輸入-輸出穩定性、無源性和反饋系統的頻域分析；現代分析部分介紹了現代穩定性分析的基本概念、擾動系統的穩定性、擾動理論和平均化以及奇異擾動理論；非線性反饋控制部分介紹了反饋線性化，并給出了幾種非線性設計工具，如滑�？刂�、李雅普諾夫再設計、反步設計法、基于無源性的控制和高增益觀測器等。此外本書附錄還匯集了一些書中用到的數學知識，包括基本數學知識的復習、壓縮映射和一些較為復雜的定理證明。本書已根據作者于2017年2月更新過的勘誤表進行過更正。
美國密歇根大學電氣與計算機工程系University Distinguished教授。1989年由于其在“奇異擾動理論及其在控制中的應用”方面的成就被選為IEEE會士。多年來一直從事非線性系統的教學和研究工作，主要研究方向包括非線性（魯棒和自適應）控制、奇異擾動理論和電驅動控制。本書第二版曾于2002年獲國際自動控制聯合會（IFAC）授予的控制工程教材獎。
美國密歇根大學電氣與計算機工程系University Distinguished教授。1989年由于其在“奇異擾動理論及其在控制中的應用”方面的成就被選為IEEE會士。多年來一直從事非線性系統的教學和研究工作，主要研究方向包括非線性（魯棒和自適應）控制、奇異擾動理論和電驅動控制。本書第二版曾于2002年獲國際自動控制聯合會（IFAC）授予的控制工程教材獎。
Contents
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 L1 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 Lyapunov 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 Linearization
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 Lyapunov 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
Note and References
Bibliography
Symbols
Index
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