Wu / He / She Stability Analysis and Robust Control of Time-Delay Systems

1. Auflage 2010
ISBN: 978-3-642-03037-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 335 Seiten

'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.

Autoren/Hrsg.

Wu, Min

He, Yong

She, Jin-Hua

Inhaltsverzeichnis

1;Preface;5
2;Table of Contents;7
3;Abbreviations;13
4;Symbols;14
5;1. Introduction;16
5.1;1.1 Review of Stability Analysis for Time-Delay Systems;16
5.1.1;Model transformation I;20
5.1.2;Model transformation II;21
5.1.3;Model transformation III;22
5.1.4;Model transformation IV;22
5.2;1.2 Introduction to FWMs;26
5.3;1.3 Outline of This Book;27
5.4;References;30
6;2. Preliminaries;34
6.1;2.1 Lyapunov Stability and Basic Theorems;34
6.1.1;2.1.1 Types of Stability;34
6.1.1.1;1) Continuous-Time Systems;34
6.1.1.2;2) Discrete-Time Systems;36
6.1.2;2.1.2 Lyapunov Stability Theorems;37
6.2;2.2 Stability of Time-Delay Systems;40
6.2.1;2.2.1 Stability-Related Topics;40
6.2.1.1;1) Time-Delay Systems;40
6.2.1.2;2) Functional Differential Equations;41
6.2.1.3;3) Concept of Stability;42
6.2.2;2.2.2 Lyapunov-Krasovskii Stability Theorem;43
6.2.3;2.2.3 Razumikhin Stability Theorem;44
6.3;2.3 H8 Norm;45
6.3.1;2.3.1 Norm;45
6.3.2;2.3.2 H8 Norm;46
6.4;2.4 H8 Control;47
6.5;2.5 LMI Method;49
6.5.1;2.5.1 Common Specifications of LMIs;49
6.5.2;2.5.2 Standard LMI Problems;50
6.6;2.6 Lemmas;51
6.7;2.7 Conclusion;53
6.8;References;53
7;3. Stability of Systems with Time-Varying Delay;55
7.1;3.1 Problem Formulation;57
7.2;3.2 Stability of Nominal System;58
7.2.1;3.2.1 Replacing the Term x(t);58
7.2.2;3.2.2 Retaining the Term x(t);61
7.2.3;3.2.3 Equivalence Analysis ;64
7.3;3.3 Stability of Systems with Time-Varying Structured Uncertainties;65
7.3.1;3.3.1 Robust Stability Analysis;65
7.3.2;3.3.2 Numerical Example;67
7.4;3.4 Stability of Systems with Polytopic-Type Uncertainties;68
7.4.1;3.4.1 Robust Stability Analysis;68
7.4.2;3.4.2 Numerical Example;71
7.5;3.5 IFWM Approach;72
7.5.1;3.5.1 Retaining Useful Terms;73
7.5.2;3.5.2 Further Investigation;78
7.5.3;3.5.3 Numerical Examples;80
7.6;3.6 Conclusion;82
7.7;References;82
8;4. Stability of Systems with Multiple Delays;86
8.1;4.1 Problem Formulation;87
8.2;4.2 Two Delays;88
8.2.1;4.2.1 Nominal Systems;88
8.2.2;4.2.2 Equivalence Analysis;94
8.2.3;4.2.3 Systems with Time-Varying Structured Uncertainties;96
8.2.4;4.2.4 Numerical Examples;98
8.3;4.3 Multiple Delays;102
8.4;4.4 Conclusion;104
8.5;References;105
9;5. Stability of Neutral Systems;106
9.1;5.1 Neutral Systems with Time-Varying Discrete Delay;107
9.1.1;5.1.1 Problem Formulation;107
9.1.2;5.1.2 Nominal Systems;108
9.1.3;5.1.3 Systems with Time-Varying Structured Uncertainties;113
9.1.4;5.1.4 Numerical Example;114
9.2;5.2 Neutral Systems with Identical Discrete and Neutral Delays;114
9.2.1;5.2.1 FWM Approach;115
9.2.2;5.2.2 FWM Approach in Combination with Parameterized Model Transformation;118
9.2.3;5.2.3 FWM Approach in Combination with Augmented Lyapunov- Krasovskii Functional;122
9.2.4;5.2.4 Numerical Examples ;127
9.3;5.3 Neutral Systems with Different Discrete and Neutral Delays;129
9.3.1;5.3.1 Nominal Systems;129
9.3.2;5.3.2 Equivalence Analysis;133
9.3.3;5.3.3 Systems with Time-Varying Structured Uncertainties;134
9.3.4;5.3.4 Numerical Example;135
9.4;5.4 Conclusion;136
9.5;References;136
10;6. Stabilization of Systems with Time-Varying Delay;139
10.1;6.1 Problem Formulation;140
10.2;6.2 Iterative Nonlinear Minimization Algorithm;141
10.3;6.3 Parameter-Tuning Method;148
10.4;6.4 Completely LMI-Based Design Method;150
10.5;6.5 Numerical Example;153
10.6;6.6 Conclusion;157
10.7;References;157
11;7. Stability and Stabilization of Discrete-Time Systems with Time-Varying Delay;159
11.1;7.1 Problem Formulation;160
11.2;7.2 Stability Analysis;161
11.3;7.3 Controller Design;165
11.3.1;7.3.1 SOF Controller;166
11.3.2;7.3.2 DOF Controller;168
11.4;7.4 Numerical Examples;170
11.5;7.5 Conclusion;171
11.6;References;171
12;8. H8 Control Design for Systems with Time-Varying Delay;174
12.1;8.1 Problem Formulation;174
12.2;8.2 BRL;176
12.3;8.3 Design of State-Feedback H8 Controller;179
12.4;8.4 Numerical Examples;182
12.5;8.5 Conclusion;184
12.6;References;185
13;9. H8 Filter Design for Systems with Time-Varying Delay;187
13.1;9.1 H8 Filter Design for Continuous-Time Systems;188
13.1.1;9.1.1 Problem Formulation;188
13.1.2;9.1.2 H8 Performance Analysis ;190
13.1.3;9.1.3 Design of H8 Filter;194
13.1.4;9.1.4 Numerical Examples;197
13.2;9.2 H8 Filter Design for Discrete-Time Systems;198
13.2.1;9.2.1 Problem Formulation;198
13.2.2;9.2.2 H8 Performance Analysis;200
13.2.3;9.2.3 Design of H8 Filter;207
13.2.4;9.2.4 Numerical Example;209
13.3;9.3 Conclusion;210
13.4;References;210
14;10. Stability of Neural Networks with Time-Varying Delay;213
14.1;10.1 Stability of Neural Networks with Multiple Delays;215
14.1.1;10.1.1 Problem Formulation;215
14.1.2;10.1.2 Stability Criteria;216
14.1.3;10.1.3 Numerical Examples;223
14.2;10.2 Stability of Neural Networks with Interval Delay;225
14.2.1;10.2.1 Problem Formulation;225
14.2.2;10.2.2 Stability Criteria;226
14.2.3;10.2.3 Numerical Examples;231
14.3;10.3 Exponential Stability of Continuous-Time Neural Networks;233
14.3.1;10.3.1 Problem Formulation;233
14.3.2;10.3.2 Stability Criteria Derived by FWM Approach;234
14.3.3;10.3.3 Stability Criteria Derived by IFWM Approach;240
14.3.4;10.3.4 Numerical Examples;245
14.4;10.4 Exponential Stability of Discrete-Time Recurrent Neural Networks;247
14.4.1;10.4.1 Problem Formulation;247
14.4.2;10.4.2 Stability Criterion Derived by IFWM Approach;248
14.4.3;10.4.3 Numerical Examples;255
14.5;10.5 Conclusion;256
14.6;References;257
15;11. Stability of T-S Fuzzy Systems with Time-Varying Delay;260
15.1;11.1 Problem Formulation;261
15.2;11.2 Stability Analysis;262
15.3;11.3 Numerical Examples;267
15.4;11.4 Conclusion;269
15.5;References;269
16;12. Stability and Stabilization of NCSs;272
16.1;12.1 Modeling of NCSs with Network-Induced Delay;273
16.2;12.2 Stability Analysis;275
16.3;12.3 Controller Design;278
16.4;12.4 Numerical Examples;280
16.5;12.5 Conclusion;281
16.6;References;282
17;13. Stability of Stochastic Systems with Time-Varying Delay;285
17.1;13.1 Robust Stability of Uncertain Stochastic Systems;286
17.1.1;13.1.1 Problem Formulation;286
17.1.2;13.1.2 Robust Stability Analysis;287
17.1.3;13.1.3 Numerical Example;291
17.2;13.2 Exponential Stability of Stochastic Markovian Jump Systems with Nonlinearities;292
17.2.1;13.2.1 Problem Formulation;292
17.2.2;13.2.2 Exponential-Stability Analysis;294
17.2.3;13.2.3 Numerical Example;302
17.3;13.3 Conclusion;303
17.4;References;304
18;14. Stability of Nonlinear Time-Delay Systems;306
18.1;14.1 Absolute Stability of Nonlinear Systems with Delay and Multiple Nonlinearities;308
18.1.1;14.1.1 Problem Formulation;308
18.1.2;14.1.2 Nominal Systems;310
18.1.3;14.1.3 Systems with Time-Varying Structured Uncertainties;315
18.1.4;14.1.4 Numerical Examples;317
18.2;14.2 Absolute Stability of Nonlinear Systems with Time-Varying Delay;318
18.2.1;14.2.1 Problem Formulation;319
18.2.2;14.2.2 Nominal Systems;320
18.2.3;14.2.3 Systems with Time-Varying Structured Uncertainties;323
18.2.4;14.2.4 Numerical Example;324
18.3;14.3 Stability of Systems with Interval Delay and Nonlinear Perturbations;325
18.3.1;14.3.1 Problem Formulation;325
18.3.2;14.3.2 Stability Results;326
18.3.3;14.3.3 Further Results Obtained with Augmented Lyapunov-Krasovskii Functional;332
18.3.4;14.3.4 Numerical Examples;337
18.4;14.4 Conclusion;337
18.5;References;338
19;Index;342