非线性控制系统的分析与设计（英文版）
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, Chows 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 LaSalles Invariance Principle
7.5 Converse Theorems to Lyapunovs 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 Lure 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 Morgans 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 LaSalles 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 Sards 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
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, Chows 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 LaSalles Invariance Principle
7.5 Converse Theorems to Lyapunovs 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 Lure 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 Morgans 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 LaSalles 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 Sards 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
Dr. Daizhan Cheng， a professor at Institute of Systems Science， Chinese Academy of Sciences， has been working on the control of nonlinear systems for over 30 years and is currently a Fellow of IEEE and a Fellow of IFAC， he is also the chairman of Technical Committee on Control Theory， Chinese Association of Automation.
《非线性控制系统的分析与设计(英文版)》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《非线性控制系统的分析与设计(英文版)》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。 《非线性控制系统的分析与设计(英文版)》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。
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