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E-raamat: Analysis and Control of Nonlinear Systems with Stationary Sets: Time-Domain and Frequency-Domain Methods [World Scientific e-raamat]

(Peking Univ, China), (Peking Univ, China), (Peking Univ, China), (Peking Univ, China)
  • Formaat: 334 pages
  • Ilmumisaeg: 16-Mar-2009
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789812814715
Teised raamatud teemal:
  • World Scientific e-raamat
  • Hind: 123,82 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Analysis and Control of Nonlinear Systems with Stationary Sets: Time-Domain and Frequency-Domain MethodsSuurem pilt
  • Formaat: 334 pages
  • Ilmumisaeg: 16-Mar-2009
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789812814715
Teised raamatud teemal:
World Scientific e-raamatudRohkem infot World Scientific e-raamatute kohta
Raamatu kodulehekülg: http://www.worldscientific.com/worldscibooks/10.1142/6862#t=toc
Nonlinear systems with stationary sets are important because they cover a lot of practical systems in engineering. Previous analysis has been based on the frequency-domain for this class of systems. However, few results on robustness analysis and controller design for these systems are easily available.This book presents the analysis as well as methods based on the global properties of systems with stationary sets in a unified time-domain and frequency-domain framework. The focus is on multi-input and multi-output systems, compared to previous publications which considered only single-input and single-output systems. The control methods presented in this book will be valuable for research on nonlinear systems with stationary sets.
Preface v
Notation and Symbols xxi
Linear Systems and Linear Matrix Inequalities
1(22)
Controllability and observability of linear systems
1(6)
Controllability and observability
2(4)
Stabilizability and detectability
6(1)
Algebraic Lyapunov equations and Lyapunov inequalities
7(5)
Continuous-time algebraic Lyapunov equations
7(3)
Continuous-time Lyapunov inequalities
10(1)
Discrete-time algebraic Lyapunov equations and inequalities
11(1)
Formulation related to linear matrix inequalities
12(3)
Schur complements
12(1)
Projection lemma
13(2)
The S-procedure
15(1)
The S-procedure for nonstrict inequalities
15(1)
The S-procedure for strict inequalities
15(1)
Kalman-Yakubovic-Popov (KYP) lemma and its generalized forms
16(5)
Notes and references
21(2)
LMI Approach to H∞ Control
23(22)
L∞ norm and H∞ norm of the systems
23(4)
L∞ and H∞ spaces
24(1)
Computing L∞ and H∞ norms
25(2)
Linear fractional transformations
27(2)
Redheffer star product
29(1)
Algebraic Riccati equations
30(4)
Solvability conditions for Riccati equations
31(2)
Discrete Riccati equations
33(1)
Bounded real lemma
34(2)
Small gain theorem
36(1)
LMI approach to H∞ control
37(6)
Continuous-time H∞ control
37(5)
Discrete-time H∞ control
42(1)
Notes and references
43(2)
Analysis and Control of Positive Real Systems
45(30)
Positive real systems
45(7)
Positive real lemma
52(11)
LMI approach to control of SPR
63(3)
Relationship between SPR control and SBR control
66(3)
Multiplier design for SPR
69(4)
Notes and references
73(2)
Absolute Stability and Dichotomy of Lur'e Systems
75(24)
Circle criterion of SISO Lur'e systems
75(5)
Popov criterion of SISO Lur'e systems
80(2)
Aizerman and Kalman conjectures
82(2)
MIMO Lur'e systems
84(5)
Dichotomy of Lur'e systems
89(4)
Bounded derivative conditions
93(4)
Notes and references
97(2)
Pendulum-like Feedback Systems
99(32)
Several examples
99(3)
Pendulum-like feedback systems
102(5)
The first canonical form of pendulum-like feedback system
103(2)
The second canonical form of pendulum-like feedback system
105(1)
The relationship between the first and the second forms of pendulum-like feedback systems
106(1)
Dichotomy of pendulum-like feedback systems
107(7)
Dichotomy of the second form of autonomous pendulum-like feedback systems
107(5)
Dichotomy of the first form of pendulum-like feedback systems
112(2)
Gradient-like property of pendulum-like feedback systems
114(4)
Gradient-like property of the second form of pendulum-like feedback systems
114(3)
Gradient-like property of the first form of pendulum-like feedback systems
117(1)
Lagrange stability of pendulum-like feedback systems
118(6)
Bakaev stability of pendulum-like feedback systems
124(5)
Notes and references
129(2)
Controller Design for a Class of Pendulum-like Systems
131(18)
Controller design with dichotomy or gradient-like property
131(8)
Controller design with dichotomy
131(6)
Controller design with gradient-like property
137(2)
Controller design with Lagrange stability
139(8)
Notes and references
147(2)
Controller Designs for Systems with Input Nonlinearities
149(14)
Lagrange stabilizing for systems with input nonlinearities
149(6)
Bakaev stabilizing for systems with input nonlinearities
155(4)
Control for systems with input nonlinearities guaranteeing dichotomy
159(3)
Notes and references
162(1)
Analysis and Control for Uncertain Feedback Nonlinear Systems
163(44)
Dichotomy of systems with norm bounded uncertainties
163(11)
Robust analysis for dichotomy
164(4)
Robust control for systems with dichotomy
168(6)
Dichotomy of pendulum-like systems with uncertainties
174(5)
Controller design with dichotomy for uncertain pendulum-like systems
179(5)
Lagrange stability for uncertain pendulum-like systems
184(3)
Gradient-like property for pendulum-like systems with uncertainties
187(4)
Control of uncertain systems guaranteeing gradient-like property
191(8)
Gradient-like property of systems with norm bounded uncertainties
199(6)
Notes and references
205(2)
Control of Periodic Oscillations in Nonlinear Systems
207(30)
Periodic solutions in systems with cylindrical phase space
207(4)
Nonexistence of periodic solutions in Lur'e systems
211(7)
LMI-based conditions for nonexistence of periodic solutions
211(2)
Robustness analysis
213(1)
Robust synthesis
214(4)
Nonexistence of cycles of the second kind in interconnected systems
218(10)
Nonexistence of cycles of the second kind in interconnected systems
220(4)
Nonlinear interconnection design
224(4)
Cycle slipping in phase synchronization systems
228(8)
Notes and references
236(1)
Interconnected Systems
237(30)
Linearly interconnected systems
238(12)
The effect of the unstable subsystem
238(3)
Interconnected feedbacks
241(3)
Decentralized controller design
244(2)
The effect of small gain theorem
246(4)
Interconnected Lur'e systems
250(2)
Lagrange stability of a generalized smooth Chua circuit
252(5)
Input and output coupled nonlinear systems
257(7)
Notes and references
264(3)
Chua's Circuit
267(28)
Chua's circuit
267(3)
Dichotomy: application to chaos control for Chua's circuit system
270(10)
Kalman conjecture: application to the stabilization of Chua's circuit
280(6)
An extended Chua circuit
286(2)
Coupled Chua circuit
288(5)
Notes and references
293(2)
Bibliography 295(14)
Index 309
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