非線性系統(tǒng)

內(nèi)容概要

　　本非線性系統(tǒng)的研究近年來受到越來越廣泛的關(guān)注，國外許多工科院校已將“非線性系統(tǒng)”作為相關(guān)專業(yè)研究生的學位課程。本書是美國密歇根州立大學電氣與計算機工程專業(yè)的研究生教材，全書內(nèi)容按照數(shù)學知識的由淺入深分成了四個部分。基本分析部分介紹了非線性系統(tǒng)的基本概念和基本分析方法；反饋系統(tǒng)分析部分介紹了輸入-輸出穩(wěn)定性、無源性和反饋系統(tǒng)的頻域分析；現(xiàn)代分析部分介紹了現(xiàn)代穩(wěn)定性分析的基本概念、擾動系統(tǒng)的穩(wěn)定性、擾動理論和平均化以及奇異擾動理論；非線性反饋控制部分介紹了反饋線性化，并給出了幾種非線性設(shè)計工具，如滑模控制、李雅普諾夫再設(shè)計、反步設(shè)計法、基于無源性的控制和高增益觀測器等。此外本書附錄還匯集了一些書中用到的數(shù)學知識，包括基本數(shù)學知識的復(fù)習、壓縮映射和一些較為復(fù)雜的定理證明。本書已根據(jù)作者于2012年4月2日更新過的勘誤表進行過更正。

作者簡介

作者:Hassan K. Khalil（哈森 K. 哈里爾）

書籍目錄

1 introduction
1.1 nonlinear models and nonlinear phenomena
1.2 examples
1.2.1 pendulum equation
1.2.2 tunnel-diode circuit
1.2.3 mass-spring system
1.2.4 negative-resistance oscillator1.2.5 artificial neural network
1.2.6 adaptive control
1.2.7 common nonlinearities
1.3 exercises
2 second-order systems
2.1 qualitative behavior of linear systems
2.2 multiple equilibria
2.3 qualitative behavior near equilibrium points
2.4 limit cycles
2.5 numerical construction of phase portraits
2.6 existence of periodic orbits
2.7 bifurcation
2.8 exercises
3 fundamental properties
3.1 existence and uniqueness
3.2 continuous dependence on initial conditions and
parameters
3.3 differentiability of solutions and sensitivity equations
3.4 comparison principle
3.5 exercises
4 lyapunov stability
4.1 autonomous systems
4.2 the invariance principle
4.3 linear systems and linearization
4 4 comparison functions
4.5 nonautonomous systems
4.6 linear time-varying systems and linearization
4.7 converse theorems
4.8 boundedness and ultimate boundedness
4 9 input-to-state stability
4.10 exercises
5 input-output stability
5.1 l stability
5.2 l stability of state models
5.3 l2 gain
5.4 feedback systems: the small-gain theorem
5.5 exercises
6 passivity
6.1 memoryless functions
6.2 state models
6.3 positive real transfer functions
6.4 l2 and lyapunov stability
6.5 feedback systems: passivity theorems
6.6 exercises
7 frequency domain analysis of feedback systems
7.1 absolute stability
7.1.1 circle criterion
7.1.2 popov criterion
7.2 the describing function method
7.3 exercises
8 advanced stability analysis
8.1 the center manifold theorem
8.2 region of attraction
8 3 invariance-like theorems
8.4 stability of periodic solutions
8.5 exercises
9 stability of perturbed systems
9.1 vanishing perturbation
9.2 nenvanishing perturbation
9.3 comparison method
9.4 continuity of solutions on the infinite interval
9.5 interconnected systems
9.6 slowly varying systems
9.7 exercises
10 perturbation theory and averaging
10.1 the perturbation method
10.2 perturbation on the infinite interval
10.3 periodic perturbation of autonomous systems
10.4 averaging
10.5 weakly nonlinear second-order oscillators
10.6 general averaging
10.7 exercises
11 singular perturbations
11.1 tlie standard singular perturbation model
11.2 time-scale properties of the standard model
11.3 singular perturbation on the infinite interval
11.4 slow and fast manifolds
11.5 stability analysis
11.6 exercises
12 feedback control
12.1 control problems
12.2 stabilization via hinearization
12.3 integral control
12.4 integral control via linearization
12.5 gain scheduling
12.6 exercises
13 feedback linearization
13.1 motivation
13.2 input-output linearization
13.3 full-state linearization
13.4 state feedback control
13.4.1 stabilization
13.4.2 tracking
13.5 exercises
14 nonlinear design tools
14.1 sliding mode control
14.1.1 motivating example
14.1.2 stabilization
14.1.3 tracking
14.1.4 regulation via integral control
14.2 lyapunov redesign
14.2.1 stabilization
14.2.2 nonlinear damping
14.3 backstepping
14.4 passivity-based control
14.5 high-gain observers
14.5.1 motivating example
14.5.2 stabilization
14.5.3 regulation via integral control
14.6 exercises
a mathematical review
b contraction mapping
c proofs
c.1 proof of theorems 3.1 and 3.2
c.2 proof of lemma 3.4
c.3 proof of lemma 4.1
c.4 proof of lemma 4.3
c.5 proof of lemma 4.4
c.6 proof of lemma 4.5
c.7 proof of theorem 4.16
c.8 proof of theorem 4.17
c.9 proof of theorem 4.18
c.10 proof of theorem 5.4
c.11 proof of lemma 6.1
c.12 proof of lemma 6.2
c.13 proof of lemma 7.1
c.14 proof of theorem 7.4
c.15 proof of theorems 8.1 and 8.3
c 16 proof of lemma 8 1
c.17 proof of theorem 11.1
c.18 proof of theorem 11.2
c.19 proof of theorem 12.1
c.20 proof of theorem 12.2
c.21 proof of theorem 13.1
c.22 proof of theorem 13.2
c.23 proof of theorem 14.6
note and references
bibliography
symbols
index

章節(jié)摘錄

版權(quán)頁：   插圖：   Chapter 4 Lyapunov Stability Stability theory plays a central role in systems theory and engineering.There are different kinds of stability problems that arise in the study of dynamical systems.This chapter is concerned mainly with stability of equilibrium points.In later chapters,we shall see other kinds of stability,such as input-output stability and stability of periodic orbits.Stability of equilibrium points is usually characterized in the sense of Lyapunov,a Russian mathematician and engineer who laid the foundation of the theory,which now carries his name.An equilibrium point is stable if all solutions starting at nearby points stay nearby; otherwise,it is unstable.It is asymptotically stable if all solutions starting at nearby points not only stay nearby,but also tend to the equilibrium point as time approaches infinity.These notions are made precise in Section 4.1,where the basic theorems of Lyapunov's method for autonomous systems are given.An extension of the basic theory,due to LaSalle,is given in Section 4.2.For a linear time-invariant system (x)(t) = Ax(t),the stability of the equilibrium point x = 0 can be completely characterized by the location of the eigenvalues of A.This is discussed in Section 4.3.In the same section,it is shown when and how the stability of an equilibrium point can be determined by linearization about that point.In Section 4.4,we introduce class K.and class K.L functions,which are used extensively in the rest of the chapter,and indeed the rest of the book.In Sections 4.5 and 4.6,we extend Lyapunov's method to nonautonomous systems.In Section 4.5,we define the concepts of uniform stability,uniform asymptotic stability,and exponential stability for nonautonomous systems,and give Lyapunov's method for testing them.In Section 4.6,we study linear timevarying systems and linearization.

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《國外計算機科學教材系列:非線性系統(tǒng)(第3版)(英文版)》既可以作為研究第一學期非線性系統(tǒng)課程的教材，也可以作為工程技術(shù)人員、應(yīng)用數(shù)學專業(yè)人員的自學教材或參考書。

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