非線性繫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“非線性繫統”作為相關專業研究生的學位課程。本書介紹了非線性繫統的基本概念和基本分析方法；輸入-輸出穩定性、無源性和反饋繫統的頻域分析；現代穩定性分析的基本概念、擾動繫統的穩定性、擾動理論和平均化以及奇異擾動理論；反饋控制的基本概念的反饋線性化，並給出了幾種非線性設計工具，如滑模控制、Lyapunov再設計、反步法、基於無源的控制和高增益觀測器等。此外本書附錄還彙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。
本書既可以作為研究生**學期非線性繫統課程的教材，也可以作為工程技術人員、應用數學專業人員的自學教材或參考書。

Preface
Acknowledgments
Standard Notation
1 Linear vs. Nonlinear
　1.1 Nonlinear Models
　1.2 Complexity in Nonlinear Dynamics
　　1.2.1 Subtleties of Nonlinear Systems Analysis
　　1.2.2 Autonomous Systems and Equilibrium Points
　1.3 Some Classical Examples
　　1.3.1 The Tunnel Diode Circuit
　　1.3.2 An Oscillating Circuit: Due to van der Po!
　　1.3.3 The Pendulum: Due to Newton
　　1.3.4 The Buckling Beam: Due to Euler
　　1.3.5 The Volterra-Lotka Predator-Prey Equations
　1.4 Other Classics: Musical Instruments
　　1.4.1 Blowing of a Clarinet Reed: Due to Rayleigh
　　1.4.2 Bowing of a Violin String: Due to Rayleigh
　1.5 Summary
　1.6 Exercises
2 Planar Dynamical Systems
　2.1 Introduction
　2.2 Linearization About Equilibria of Second-Order Nonlinear Systems
　　2.2.1 Linear Systems in the Plane
　　2.2.2 Phase Portraits near Hyperbolic Equilibria
　2.3 Closed Orbits of Planar Dynamical Systems
　2.4 Counting Equilibria: Index Theory
　2.5 Bifurcations
　2.6 Bifurcation Study of Josephson Junction Equations
　2.7 The Degenerate van der Pol Equation
　2.8 Planar Discrete-Time Systems
　　2.8.1 Fixed Points and the Hartman-Grobman Theorem
　　2.8.2 Period N Points of Maps
　　2.8.3 Bifurcations of Maps
　2.9 Summary
　2.10 Exercises
3 Mathematical Background
　3.1 Groups and Fields
　3.2 Vector Spaces, Algebras, Norms, and Induced Norms
　3.3 Contraction Mapping Theorems
　　3.3.1 Incremental Small Gain Theorem
　3.4 Existence and Uniqueness Theorems for Ordinary Differential Equations
　　3.4.1 Dependence on Initial Conditions on Infinite Time Intervals
　　3.4.2 Circuit Simulation by Waveform Relaxation
　3.5 Differential Equations with Discontinuities
　3.6 Carleman Linearization
　3.7 Degree Theory
　3.8 Degree Theory and Solutions of Resistive Networks
　3.9 Basics of Differential Topology
　　3.9.1 Smooth Manifolds and Smooth Maps
　　3.9.2 Tangent Spaces and Derivatives
　　3.9.3 Regular Values
　　3.9.4 Manifolds with Boundary
　3.10 Summary
　3.11 Exercises
4 Input-Output Analysis
5 Lyapunov Stability THeory
6 Applications of Lyapunov THeory
7 Dynamical Systems and Bifurcations
8 Basics of Differential Geometry
9 Linearization by State Feedback
10 Design Examples Using Linearization
11 Geometric Nonlinear Control
12 Exterior Differential Systems in Control
13 New Vistas: Multi-Agent Hybrid Systems
References
Index