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| 內容簡介： |
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本非线性系统的研究近年来受到越来越广泛的关注，国外许多工科院校已将“非线性系统”作为相关专业研究生的学位课程。本书是美国密歇根州立大学电气与计算机工程专业的研究生教材，全书内容按照数学知识的由浅入深分成了四个部分。基本分析部分介绍了非线性系统的基本概念和基本分析方法；反馈系统分析部分介绍了输入-输出稳定性、无源性和反馈系统的频域分析；现代分析部分介绍了现代稳定性分析的基本概念、扰动系统的稳定性、扰动理论和平均化以及奇异扰动理论；非线性反馈控制部分介绍了反馈线性化，并给出了几种非线性设计工具，如滑模控制、李雅普诺夫再设计、反步设计法、基于无源性的控制和高增益观测器等。此外本书附录还汇集了一些书中用到的数学知识，包括基本数学知识的复习、压缩映射和一些较为复杂的定理证明。本书已根据作者于2012年4月2日更新过的勘误表进行过更正。
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| 目錄：
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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
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