非线性系统

内容概要

作者：(美国)萨斯特

书籍目录

PrefaceAcknowledgmentsStandard Notation1 Linear vs. Nonlinear1.1 Nonlinear Models1.2 Complexity in Nonlinear Dynamics1.2.1 Subtleties of Nonlinear Systems Analysis1.2.2 Autonomous Systems and Equilibrium Points1.3 Some Classical Examples1.3.1 The Tunnel Diode Circuit1.3.2 An Oscillating Circuit: Due to van der Po!1.3.3 The Pendulum: Due to Newton1.3.4 The Buckling Beam: Due to Euler1.3.5 The Volterra-Lotka Predator-Prey Equations1.4 Other Classics: Musical Instruments1.4.1 Blowing of a Clarinet Reed: Due to Rayleigh1.4.2 Bowing of a Violin String: Due to Rayleigh1.5 Summary1.6 Exercises2 Planar Dynamical Systems2.1 Introduction2.2 Linearization About Equilibria of Second-Order Nonlinear Systems2.2.1 Linear Systems in the Plane2.2.2 Phase Portraits near Hyperbolic Equilibria2.3 Closed Orbits of Planar Dynamical Systems2.4 Counting Equilibria: Index Theory2.5 Bifurcations2.6 Bifurcation Study of Josephson Junction Equations2.7 The Degenerate van der Pol Equation2.8 Planar Discrete-Time Systems2.8.1 Fixed Points and the Hartman-Grobman Theorem2.8.2 Period N Points of Maps2.8.3 Bifurcations of Maps2.9 Summary2.10 Exercises3 Mathematical Background3.1 Groups and Fields3.2 Vector Spaces, Algebras, Norms, and Induced Norms3.3 Contraction Mapping Theorems3.3.1 Incremental Small Gain Theorem3.4 Existence and Uniqueness Theorems for Ordinary Differential Equations3.4.1 Dependence on Initial Conditions on Infinite Time Intervals3.4.2 Circuit Simulation by Waveform Relaxation3.5 Differential Equations with Discontinuities3.6 Carleman Linearization3.7 Degree Theory3.8 Degree Theory and Solutions of Resistive Networks3.9 Basics of Differential Topology3.9.1 Smooth Manifolds and Smooth Maps3.9.2 Tangent Spaces and Derivatives3.9.3 Regular Values3.9.4 Manifolds with Boundary3.10 Summary3.11 Exercises4 Input-Output Analysis4.1 Optimal Linear Approximants to Nonlinear Systems4.1.1 Optimal Linear Approximations for Memoryless, Time-Invariant Nonlinearities4.1.2 Optimal Linear Approximations for Dynamic Nonlinearities: Oscillations in Feedback Loops4.1.3 Justification of the Describing Function4.2 Input-Output Stability.4.3 Applications of the Small Gain Theorems……5 Lyapunov Stability THeory6 Applications of Lyapunov THeory7 Dynamical Systems and Bifurcations8 Basics of Differential Geometry9 Linearization by State Feedback10 Design Examples Using Linearization11 Geometric Nonlinear Control12 Exterior Differential Systems in Control13 New Vistas: Multi-Agent Hybrid SystemsReferencesIndex

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《非线性系统》由世界图书出版公司出版。

作者简介

《非线性系统》简要介绍了分析的方法和工具。近十年来非线性系统中分析与控制出现了许多新的数学工具，几何非线性控制的综合理论也有较大发展，基于此，非线性系统模拟和精密实时非线性控制律的计算功能有了巨大的进步。这种技巧上的发展促进了分析方法的发展。

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