内容简介
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。
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. 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 Expa
