Analysis and control of nonlinear systems with stationary sets : time-domain and frequency-domain methods

Title:

Publication Information:

New Jersey : World Scientific Publishing Company, 2009

Physical Description:

xxii, 311 p. : ill. ; 24 cm.

ISBN:

9789812814692

Subject Term:

Nonlinear control theory

Added Author:

Wang, Jinzhi

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010197071	QA402.35 A52 2009	Open Access Book	Book	Searching... Unknown

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	p. v
Notation and Symbols	p. xxi
1 Linear Systems and Linear Matrix Inequalities	p. 1
1.1 Controllability and observability of linear systems	p. 1
1.1.1 Controllability and observability	p. 2
1.1.2 Stabilizability and detectability	p. 6
1.2 Algebraic Lyapunov equations and Lyapunov inequalities	p. 7
1.2.1 Continuous-time algebraic Lyapunov equations	p. 7
1.2.2 Continuous-time Lyapunov inequalities	p. 10
1.2.3 Discrete-time algebraic Lyapunov equations and inequalities	p. 11
1.3 Formulation related to linear matrix inequalities	p. 12
1.3.1 Schur complements	p. 12
1.3.2 Projection lemma	p. 13
1.4 The S-procedure	p. 15
1.4.1 The S-procedure for nonstrict inequalities	p. 15
1.4.2 The S-procedure for strict inequalities	p. 15
1.5 Kalman-Yakubovic-Popov (KYP) lemma and its generalized forms	p. 16
1.6 Notes and references	p. 21
2 LMI Approach to H ∞ Control	p. 23
2.1 L ∞ norm and H ∞ norm of the systems	p. 23
2.1.1 L ∞ and H ∞ spaces	p. 24
2.1.2 Computing L ∞ and H ∞ norms	p. 25
2.2 Linear fractional transformations	p. 27
2.3 Redheffer star product	p. 29
2.4 Algebraic Riccati equations	p. 30
2.4.1 Solvability conditions for Riccati equations	p. 31
2.4.2 Discrete Riccati equations	p. 33
2.5 Bounded real lemma	p. 34
2.6 Small gain theorem	p. 36
2.7 LMI approach to H ∞ control	p. 37
2.7.1 Continuous-time H ∞ control	p. 37
2.7.2 Discrete-time H ∞ control	p. 42
2.8 Notes and references	p. 43
3 Analysis and Control of Positive Real Systems	p. 45
3.1 Positive real systems	p. 45
3.2 Positive real lemma	p. 52
3.3 LMI approach to control of SPR	p. 63
3.4 Relationship between SPR control and SBR control	p. 66
3.5 Multiplier design for SPR	p. 69
3.6 Notes and references	p. 73
4 Absolute Stability and Dichotomy of Lur'e Systems	p. 75
4.1 Circle criterion of SISO Lur'e systems	p. 75
4.2 Popov criterion of SISO Lur'e systems	p. 80
4.3 Aizerman and Kalman conjectures	p. 82
4.4 MIMO Lur'e systems	p. 84
4.5 Dichotomy of Lur'e systems	p. 89
4.6 Bounded derivative conditions	p. 93
4.7 Notes and references	p. 97
5 Pendulum-like Feedback Systems	p. 99
5.1 Several examples	p. 99
5.2 Pendulum-like feedback systems	p. 102
5.2.1 The first canonical form of pendulum-like feedback system	p. 103
5.2.2 The second canonical form of pendulum-like feed-back system	p. 105
5.2.3 The relationship between the first and the second forms of pendulum-like feedback systems	p. 106
5.3 Dichotomy of pendulum-like feedback systems	p. 107
5.3.1 Dichotomy of the second form of autonomous pendulum-like feedback systems	p. 107
5.3.2 Dichotomy of the first form of pendulum-like feedback systems	p. 112
5.4 Gradient-like property of pendulum-like feedback systems	p. 114
5.4.1 Gradient-like property of the second form of pendulum-like feedback systems	p. 114
5.4.2 Gradient-like property of the first form of pendulum-like feedback systems	p. 117
5.5 Lagrange stability of pendulum-like feedback systems	p. 118
5.6 Bakaev stability of pendulum-like feedback systems	p. 124
5.7 Notes and references	p. 129
6 Controller Design for a Class of Pendulum-like Systems	p. 131
6.1 Controller design with dichotomy or gradient-like property	p. 131
6.1.1 Controller design with dichotomy	p. 131
6.1.2 Controller design with gradient-like property	p. 137
6.2 Controller design with Lagrange stability	p. 139
6.3 Notes and references	p. 147
7 Controller Designs for Systems with Input Nonlinearities	p. 149
7.1 Lagrange stabilizing for systems with input nonlinearities	p. 149
7.2 Bakaev stabilizing for systems with input nonlinearities	p. 155
7.3 Control for systems with input nonlinearities guaranteeing dichotomy	p. 159
7.4 Notes and references	p. 162
8 Analysis and Control for Uncertain Feedback Nonlinear Systems	p. 163
8.1 Dichotomy of systems with norm bounded uncertainties	p. 163
8.1.1 Robust analysis for dichotomy	p. 164
8.1.2 Robust control for systems with dichotomy	p. 168
8.2 Dichotomy of pendulum-like systems with uncertainties	p. 174
8.3 Controller design with dichotomy for uncertain pendulum-like systems	p. 179
8.4 Lagrange stability for uncertain pendulum-like systems	p. 184
8.5 Gradient-like property for pendulum-like systems with uncertainties	p. 187
8.6 Control of uncertain systems guaranteeing gradient-like property	p. 191
8.7 Gradient-like property of systems with norm bounded uncertainties	p. 199
8.8 Notes and references	p. 205
9 Control of Periodic Oscillations in Nonlinear Systems	p. 207
9.1 Periodic solutions in systems with cylindrical phase space	p. 207
9.2 Nonexistence of periodic solutions in Lur'e systems	p. 211
9.2.1 LMI-based conditions for nonexistence of periodic solutions	p. 211
9.2.2 Robustness analysis	p. 213
9.2.3 Robust synthesis	p. 214
9.3 Nonexistence of cycles of the second kind in interconnected systems	p. 218
9.3.1 Nonexistence of cycles of the second kind in interconnected systems	p. 220
9.3.2 Nonlinear interconnection design	p. 224
9.4 Cycle slipping in phase synchronization systems	p. 228
9.5 Notes and references	p. 236
10 Interconnected Systems	p. 237
10.1 Linearly interconnected systems	p. 238
10.1.1 The effect of the unstable subsystem	p. 238
10.1.2 Interconnected feedbacks	p. 241
10.1.3 Decentralized controller design	p. 244
10.1.4 The effect of small gain theorem	p. 246
10.2 Interconnected Lur'e systems	p. 250
10.3 Lagrange stability of a generalized smooth Chua circuit	p. 252
10.4 Input and output coupled nonlinear systems	p. 257
10.5 Notes and references	p. 264
11 Chua's Circuit	p. 267
11.1 Chua's circuit	p. 267
11.2 Dichotomy: application to chaos control for Chua's circuit system	p. 270
11.3 Kalman conjecture: application to the stabilization of Chua's circuit	p. 280
11.4 An extended Chua circuit	p. 286
11.5 Coupled Chua circuit	p. 288
11.6 Notes and references	p. 293
Bibliography	p. 295
Index	p. 309

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