Language: English
ISBN/ISSN: 9787030259646
Published on: 2010-01
Soft Cover
Analysis and Design of Nonlinear Control Systems provides a comprehensive and up to date introduction to nonlinear control systems, including system analysis and major control design techniques. The book is self-contained, providing sufficient mathematical foundations for understanding the contents of each chapter. Scientists and engineers engaged in the field of Nonlinear Control Systems will find it an extremely useful handy reference book.
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
……
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
