Stability Analysis and Robust Control of Time-delay Systems

by Wu, Min; He, Yong; She, Jin-Hua

• ISBN13: 9783642030369
• ISBN10: 364203036X
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-04-01
• Publisher: Springer Verlag

Summary

"Stability Analysis and Robust Control of Time-Delay Systems" focuses on essential aspects of this field, including the stability analysis, stabilization, control design, and filtering of various time-delay systems. Primarily based on the most recent research, this monograph presents all the above areas using a free-weighting matrix approach first developed by the authors. The effectiveness of this method and its advantages over other existing ones are proven theoretically and illustrated by means of various examples. The book will give readers an overview of the latest advances in this active research area and equip them with a pioneering method for studying time-delay systems. It will be of significant interest to researchers and practitioners engaged in automatic control engineering.Prof. Min Wu, senior member of the IEEE, works at the Central South University, China.

Author Biography

Prof. Min Wu, senior member of the IEEE, works at the Central South University, China.

Table of Contents

Introduction	p. 1
Review of Stability Analysis for Time-Delay Systems	p. 1
Introduction to FWMs	p. 11
Outline of This Book	p. 12
References	p. 15
Preliminaries	p. 19
Lyapunov Stability and Basic Theorems	p. 19
Types of Stability	p. 19
Lyapunov Stability Theorems	p. 22
Stability of Time-Delay Systems	p. 25
Stability-Related Topics	p. 25
Lyapunov-Krasovskii Stability Theorem	p. 28
Razumikhin Stability Theorem	p. 29
H∞ Norm	p. 30
Norm	p. 30
H∞ Norm	p. 31
H∞ Control	p. 32
LMI Method	p. 34
Common Specifications of LMIs	p. 34
Standard LMI Problems	p. 35
Lemmas	p. 36
Conclusion	p. 38
References	p. 38
Stability of Systems with Time-Varying Delay	p. 41
Problem Formulation	p. 43
Stability of Nominal System	p. 44
Replacing the Term x(t)	p. 44
Retaining the Term x(t)	p. 47
Equivalence Analysis	p. 50
Stability of Systems with Time-Varying Structured Uncertainties	p. 51
Robust Stability Analysis	p. 51
Numerical Example	p. 53
Stability of Systems with Polytopic-Type Uncertainties	p. 54
Robust Stability Analysis	p. 54
Numerical Example	p. 57
IFWM Approach	p. 58
Retaining Useful Terms	p. 59
Further Investigation	p. 64
Numerical Examples	p. 66
Conclusion	p. 68
References	p. 68
Stability of Systems with Multiple Delays	p. 73
Problem Formulation	p. 74
Two Delays	p. 75
Nominal Systems	p. 75
Equivalence Analysis	p. 81
Systems with Time-Varying Structured Uncertainties	p. 83
Numerical Examples	p. 85
Multiple Delays	p. 89
Conclusion	p. 91
References	p. 92
Stability of Neutral Systems	p. 93
Neutral Systems with Time-Varying Discrete Delay	p. 94
Problem Formulation	p. 94
Nominal Systems	p. 95
Systems with Time-Varying Structured Uncertainties	p. 100
Numerical Example	p. 101
Neutral Systems with Identical Discrete and Neutral Delays	p. 101
FWM Approach	p. 102
FWM Approach in Combination with Parameterized Model Transformation	p. 105
FWM Approach in Combination with Augmented Lyapunov-Krasovskii Functional	p. 109
Numerical Examples	p. 114
Neutral Systems with Different Discrete and Neutral Delays	p. 116
Nominal Systems	p. 116
Equivalence Analysis	p. 120
Systems with Time-Varying Structured Uncertainties	p. 121
Numerical Example	p. 122
Conclusion	p. 123
References	p. 123
Stabilization of Systems with Time-Varying Delay	p. 127
Problem Formulation	p. 128
Iterative Nonlinear Minimization Algorithm	p. 129
Parameter-Tuning Method	p. 136
Completely LMI-Based Design Method	p. 138
Numerical Example	p. 141
Conclusion	p. 145
References	p. 145
Stability and Stabilization of Discrete-Time Systems with Time-Varying Delay	p. 147
Problem Formulation	p. 148
Stability Analysis	p. 149
Controller Design	p. 153
SOF Controller	p. 154
DOF Controller	p. 156
Numerical Examples	p. 158
Conclusion	p. 159
References	p. 159
H∞ Control Design for Systems with Time-Varying Delay	p. 163
Problem Formulation	p. 163
BRL	p. 165
Design of State-Feedback H∞ Controller	p. 168
Numerical Examples	p. 171
Conclusion	p. 173
References	p. 174
H∞ Filter Design for Systems with Time-Varying Delay	p. 177
H∞ Filter Design for Continuous-Time Systems	p. 178
Problem Formulation	p. 178
H∞ Performance Analysis	p. 180
Design of H∞ Filter	p. 184
Numerical Examples	p. 187
H∞ Filter Design for Discrete-Time Systems	p. 188
Problem Formulation	p. 188
H∞ Performance Analysis	p. 190
Design of H∞ Filter	p. 197
Numerical Example	p. 199
Conclusion	p. 200
References	p. 200
Stability of Neural Networks with Time-Varying Delay	p. 203
Stability of Neural Networks with Multiple Delays	p. 205
Problem Formulation	p. 205
Stability Criteria	p. 206
Numerical Examples	p. 213
Stability of Neural Networks with Interval Delay	p. 215
Problem Formulation	p. 215
Stability Criteria	p. 216
Numerical Examples	p. 221
Exponential Stability of Continuous-Time Neural Networks	p. 223
Problem Formulation	p. 223
Stability Criteria Derived by FWM Approach	p. 224
Stability Criteria Derived by IFWM Approach	p. 230
Numerical Examples	p. 235
Exponential Stability of Discrete-Time Recurrent Neural Networks	p. 237
Problem Formulation	p. 237
Stability Criterion Derived by IFWM Approach	p. 238
Numerical Examples	p. 245
Conclusion	p. 246
References	p. 247
Stability of T-S Fuzzy Systems with Time-Varying Delay	p. 251
Problem Formulation	p. 252
Stability Analysis	p. 253
Numerical Examples	p. 258
Conclusion	p. 260
References	p. 260
Stability and Stabilization of NCSs	p. 263
Modeling of NCSs with Network-Induced Delay	p. 264
Stability Analysis	p. 266
Controller Design	p. 269
Numerical Examples	p. 271
Conclusion	p. 272
References	p. 273
Stability of Stochastic Systems with Time-Varying Delay	p. 277
Robust Stability of Uncertain Stochastic Systems	p. 278
Problem Formulation	p. 278
Robust Stability Analysis	p. 279
Numerical Example	p. 283
Exponential Stability of Stochastic Markovian Jump Systems with Nonlinerities	p. 284
Problem Formulation	p. 284
Exponential-Stability Analysis	p. 286
Numerical Example	p. 294
Conclusion	p. 295
References	p. 296
Stability of Nonlinear Time-Delay Systems	p. 299
Absolute Stability of Nonlinear Systems with Delay and Multiple Nonlinearities	p. 301
Problem Formulation	p. 301
Nominal Systems	p. 303
Systems with Time-Varying Structured Uncertainties	p. 308
Numerical Examples	p. 310
Absolute Stability of Nonlinear Systems with Time-Varying Delay	p. 311
Problem Formulation	p. 312
Nominal Systems	p. 313
Systems with Time-Varying Structured Uncertainties	p. 316
Numerical Example	p. 317
Stability of Systems with Interval Delay and Nonlinear Perturbations	p. 318
Problem Formulation	p. 318
Stability Results	p. 319
Further Results Obtained with Augmented Lyapunov-Krasovskii Functional	p. 325
Numerical Examples	p. 330
Conclusion	p. 330
References	p. 331
Index	p. 335
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