本书全面介绍了非线性控制系统的分析与设计。全书共分为两部分。其中第一部分为第1～4章。第1章介绍了拓扑空间，第2章介绍了微流形，第3章介绍了代数、Lie群和Lie代数，它们为本书提供了研究数学背景。第二部分包括12章，即第5～16章，这些章节涵盖了可控性、可观测性、稳定性、解耦、投入产出的实现、线性化、中心流技术、输出调节、耗散系统、H∞控制、切换系统和非平稳控制等方面，并给出了有关的详细设计技术。 本书可供理工科大学自动控制专业的教师及研究生阅读，也可供自然科学和工程技术领域中相关专业的研究人员参考。

1. Introduction

 1.1 Linear Control Systems

1.1.1 Controllability, Observability

1.1.2 Invariant Subspaces

1.1.3 Zeros, Poles, Observers

1.1.4 Normal Form and Zero Dynamics

 1.2 Nonlinearity vs Linearity

1.2.1 Localization

1.2.2 Singularity

1.2.3 Complex Behaviors

 1.3 Some Examples of Nonlinear Control Systems

 References

2. Topological Space

 2.1 Metric Space

 2.2 Topological Spaces

 2.3 Continuous Mapping

 2.4 Quotient Spaces

 References

3. Differentiab!e Manifold

 3.1 Structure of Manifolds

 3.2 Fiber Bundle

 3.3 Vector Field

 3.4 One Parameter Group

 3.5 Lie Algebra of Vector Fields

 3.6 Co-tangent Space

 3.7 Lie Derivatives

 3.8 Frobenius' Theory

 3.9 Lie Series, Chow's Theorem

 3.10 Tensor Field

 3.11 Riemannian Geometry

 3.12 Symplectic Geometry

 References

4. Algebra, Lie Group and Lie Algebra

 4.1 Group

 4.2 Ring and Algebra

 4.3 Homotopy

 4.4 Fundamental Group

 4.5 Covering Space

 4.6 Lie Group

 4.7 Lie Algebra of Lie Group

 4.8 Structure of Lie Algebra

 References

5. Controllability and Observability

 5.1 Controllability of Nonlinear Systems

 5.2 Observability of Nonlinear Systems

 5.3 Kalman Decomposition

 References

6. Global Controllability of Affine Control Systems

 6.1 From Linear to Nonlinear Systems

 6.2 A Sufficient Condition

 6.3 Multi-hierarchy Case

 6.4 Codim = 1

 References

7. Stability and Stabilization

 7.1 Stability of Dynamic Systems

 7.2 Stability in the Linear Approximation

 7.3 The Direct Method of Lyapunov

7.3.1 Positive Definite Functions

7.3.2 Critical Stability

7.3.3 Instability

7.3.4 Asymptotic Stability

7.3.5 Total Stability

7.3.6 Global Stability

 7.4 LaSalle's Invariance Principle

 7.5 Converse Theorems to Lyapunov's Stability Theorems

7.5.1 Converse Theorems to Local Asymptotic Stability

7.5.2 Converse Theorem to Global Asymptotic Stability

 7.6 Stability of Invariant Set

 7.7 Input-Output Stability

7.7.1 Stability of Input-Output Mapping

7.7.2 The Lur'e Problem

7.7.3 Control Lyapunov Function

 7.8 Region of Attraction

 References

8. Deeoupling

 8.1 (f,g)-invariant Distribution

 8.2 Local Disturbance Decoupling

 8.3 Controlled Invariant Distribution

 8.4 Block Decomposition

 8.5 Feedback Decomposition

 References

9. Input-Output Structure

 9.1 Decoupling Matrix

 9.2 Morgan's Problem

 9.3 Invertibility

 9.4 Decoupling via Dynamic Feedback

 9.5 Normal Form of Nonlinear Control Systems

 9.6 Generalized Normal Form

 9.7 Fliess Functional Expansion

 9.8 Tracking via Fliess Functional Expansion

References

10. Linearization of Nonlinear Systems

 10.1 Poincare Linearization

 10.2 Linear Equivalence of Nonlinear Systems

 10.3 State Feedback Linearization

 10.4 Linearization with Outputs

 10.5 Global Linearization

 10.6 Non-regular Feedback Linearization

 References

11 Design of Center Manifold

 11.1 Center Manifold

 11.2 Stabilization of Minimum Phase Systems

 11.3 Lyapunov Function with Homogeneous Derivative

 11.4 Stabilization of Systems with Zero Center

 11.5 Stabilization of Systems with Oscillatory Center

 11.6 Stabilization Using Generalized Normal Form

 11.7 Advanced Design Techniques

 References

12 Output Regulation

 12.1 Output Regulation of Linear Systems

 12.2 Nonlinear Local Output Regulation

 12.3 Robust Local Output Regulation

 References

13 Dissipative Systems

 13.1 Dissipative Systems

 13.2 Passivity Conditions

 13.3 Passivity-based Control

 13.4 Lagrange Systems

 13.5 Hamiltonian Systems

 References

14 L2-Gain Synthesis

 14.1 H∞ Norm and//2-Gain

 14.2 H∞ Feedback Control Problem

 14.3 L2-Gain Feedback Synthesis

 14.4 Constructive Design Method

 14.5 Applications

 References

15 Switched Systems

 15.1 Common Quadratic Lyapunov Function

 15.2 Quadratic Stabilization of Planar Switched Systems

 15.3 Controllability of Switched Linear Systems

 15.4 Controllability of Switched Bilinear Systems

 15.5 LaSalle's Invariance Principle for Switched Systems

 15.6 Consensus of Multi-Agent Systems

15.6.1 Two Dimensional Agent Model with a Leader

15.6.2 n Dimensional Agent Model without Lead

 References

16 Discontinuous Dynamical Systems

 16.1 Introduction

 16.2 Filippov Framework

16.2.1 Filippov Solution

16.2.2 Lyapunov Stability Criteria

 16.3 Feedback Stabilization

16.3.1 Feedback Controller Design: Nominal Case

16.3.2 Robust Stabilization

 16.4 Design Example of Mechanical Systems

16.4.1 PD Controlled Mechanical Systems

16.4.2 Stationary Set

16.4.3 Application Example

 References

Appendix A Some Useful Theorems

 A.1 Sard's Theorem

 A.2 Rank Theorem

 References

Appendix B Semi-Tensor Product of Matrices

 B.1 A Generalized Matrix Product

 B.2 Swap Matrix

 B.3 Some Properties of Semi-Tensor Product

 B.4 Matrix Form of Polynomials

 References

Index