内容简介：

　　本书全面介绍了非线性控制系统的理论与设计，可作为控制领域科研人员、工程技术人员，以及理工科大学自动控制专业教师及研究生参考用书。

　　本书重点强调了非线性控制系统的几何方法。事实上，本书作者试图尽可能地将非线性控制理论及其设计方法置于几何框架内。本书的主旨是帮助具备工程背景的读者尽快进入动态系统，尤其是非线性系统分析与控制设计的现代几何方法的研究前沿。

　　全书分三部分，共16章。其中第一部分为第1-4章，介绍了与非线性控制理论相关的数学基础。第1章为动态系统导论，第2章介绍了拓扑空间，第3章介绍了微分流形，第4章简要介绍了抽象代数的一些基本概念。第二部分为第5-10章，是非线性控制理论的核心内容，分别涉及能控性与能观性、非线性系统的全局能控性、稳定性与镇定、解耦、输入-输出结构、非线性系统的线性化等问题。第三部分为第11-16章，讨论了一些特殊的系统和控制方法，涉及中心流形方法、输出调节、耗散系统、H_∞控制、切换系统和非光滑控制等方面。

 

英文目录：
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.DifferentiableManifold
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(G)=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.Decoupling
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 DecouplingMatrix
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 Poincaré 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 L2-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