Stability Analysis and Robust Control of Time-Delay Systems

Cover......Page 1
Stability Analysis and Robust Control of Time-Delay Systems......Page 4
9787030260055......Page 5
Preface......Page 6
Table of Contents......Page 8
Abbreviations......Page 14
Symbols......Page 16
1.1 Review of Stability Analysis for Time-Delay Systems......Page 18
1.2 Introduction to FWMs......Page 28
1.3 Outline of This Book......Page 29
References......Page 32
2.1.1 Types of Stability......Page 36
2.1.2 Lyapunov Stability Theorems......Page 39
2.2.1 Stability-Related Topics......Page 42
2.2.2 Lyapunov-Krasovskii Stability Theorem......Page 45
2.2.3 Razumikhin Stability Theorem......Page 46
2.3.1 Norm......Page 47
2.3.2 H_∞ Norm......Page 48
2.4 H_∞ Control......Page 49
2.5.1 Common Specifications of LMIs......Page 51
2.5.2 Standard LMI Problems......Page 52
2.6 Lemmas......Page 53
References......Page 55
3. Stability of Systems with Time-Varying Delay......Page 58
3.1 Problem Formulation......Page 60
3.2.1 Replacing the Term \dot{x}(t)......Page 61
3.2.2 Retaining the Term \dot{x}(t)......Page 64
3.2.3 Equivalence Analysis......Page 67
3.3.1 Robust Stability Analysis......Page 68
3.3.2 Numerical Example......Page 70
3.4.1 Robust Stability Analysis......Page 71
3.4.2 Numerical Example......Page 74
3.5 IFWM Approach......Page 75
3.5.1 Retaining Useful Terms......Page 76
3.5.2 Further Investigation......Page 81
3.5.3 Numerical Examples......Page 83
References......Page 85
4. Stability of Systems with Multiple Delays......Page 90
4.1 Problem Formulation......Page 91
4.2.1 Nominal Systems......Page 92
4.2.2 Equivalence Analysis......Page 98
4.2.3 Systems with Time-Varying Structured Uncertainties......Page 100
4.2.4 Numerical Examples......Page 102
4.3 Multiple Delays......Page 106
4.4 Conclusion......Page 108
References......Page 109
5. Stability of Neutral Systems......Page 110
5.1.1 Problem Formulation......Page 111
5.1.2 Nominal Systems......Page 112
5.1.3 Systems with Time-Varying Structured Uncertainties......Page 117
5.2 Neutral Systems with Identical Discrete and Neutral Delays......Page 118
5.2.1 FWM Approach......Page 119
5.2.2 FWM Approach in Combination with Parameterized Model Transformation......Page 122
5.2.3 FWM Approach in Combination with Augmented Lyapunov- Krasovskii Functional......Page 126
5.2.4 Numerical Examples......Page 131
5.3.1 Nominal Systems......Page 133
5.3.2 Equivalence Analysis......Page 137
5.3.3 Systems with Time-Varying Structured Uncertainties......Page 138
5.3.4 Numerical Example......Page 139
References......Page 140
6. Stabilization of Systems with Time-Varying Delay......Page 144
6.1 Problem Formulation......Page 145
6.2 Iterative Nonlinear Minimization Algorithm......Page 146
6.3 Parameter-Tuning Method......Page 153
6.4 Completely LMI-Based Design Method......Page 155
6.5 Numerical Example......Page 158
References......Page 162
7. Stability and Stabilization of Discrete-Time Systems with Time-Varying Delay......Page 164
7.1 Problem Formulation......Page 165
7.2 Stability Analysis......Page 166
7.3 Controller Design......Page 170
7.3.1 SOF Controller......Page 171
7.3.2 DOF Controller......Page 173
7.4 Numerical Examples......Page 175
References......Page 176
8.1 Problem Formulation......Page 180
8.2 BRL......Page 182
8.3 Design of State-Feedback H_∞ Controller......Page 185
8.4 Numerical Examples......Page 188
8.5 Conclusion......Page 190
References......Page 191
9. H_∞ Filter Design for Systems with Time-Varying Delay......Page 194
9.1.1 Problem Formulation......Page 195
9.1.2 H_∞ Performance Analysis......Page 197
9.1.3 Design of H_∞ Filter......Page 201
9.1.4 Numerical Examples......Page 204
9.2.1 Problem Formulation......Page 205
9.2.2 H_∞ Performance Analysis......Page 207
9.2.3 Design of H_∞ Filter......Page 214
9.2.4 Numerical Example......Page 216
References......Page 217
10. Stability of Neural Networks with Time-Varying Delay......Page 220
10.1.1 Problem Formulation......Page 222
10.1.2 Stability Criteria......Page 223
10.1.3 Numerical Examples......Page 230
10.2.1 Problem Formulation......Page 232
10.2.2 Stability Criteria......Page 233
10.2.3 Numerical Examples......Page 238
10.3.1 Problem Formulation......Page 240
10.3.2 Stability Criteria Derived by FWM Approach......Page 241
10.3.3 Stability Criteria Derived by IFWM Approach......Page 247
10.3.4 Numerical Examples......Page 252
10.4.1 Problem Formulation......Page 254
10.4.2 Stability Criterion Derived by IFWM Approach......Page 255
10.4.3 Numerical Examples......Page 262
10.5 Conclusion......Page 263
References......Page 264
11. Stability of T-S Fuzzy Systems with Time-Varying Delay......Page 268
11.1 Problem Formulation......Page 269
11.2 Stability Analysis......Page 270
11.3 Numerical Examples......Page 275
References......Page 277
12. Stability and Stabilization of NCSs......Page 280
12.1 Modeling of NCSs with Network-Induced Delay......Page 281
12.2 Stability Analysis......Page 283
12.3 Controller Design......Page 286
12.4 Numerical Examples......Page 288
12.5 Conclusion......Page 289
References......Page 290
13. Stability of Stochastic Systems with Time-Varying Delay......Page 294
13.1.1 Problem Formulation......Page 295
13.1.2 Robust Stability Analysis......Page 296
13.1.3 Numerical Example......Page 300
13.2.1 Problem Formulation......Page 301
13.2.2 Exponential-Stability Analysis......Page 303
13.2.3 Numerical Example......Page 311
13.3 Conclusion......Page 312
References......Page 313
14. Stability of Nonlinear Time-Delay Systems......Page 316
14.1.1 Problem Formulation......Page 318
14.1.2 Nominal Systems......Page 320
14.1.3 Systems with Time-Varying Structured Uncertainties......Page 325
14.1.4 Numerical Examples......Page 327
14.2 Absolute Stability of Nonlinear Systems with Time-Varying Delay......Page 328
14.2.1 Problem Formulation......Page 329
14.2.2 Nominal Systems......Page 330
14.2.3 Systems with Time-Varying Structured Uncertainties......Page 333
14.2.4 Numerical Example......Page 334
14.3.1 Problem Formulation......Page 335
14.3.2 Stability Results......Page 336
14.3.3 Further Results Obtained with Augmented Lyapunov-Krasovskii Functional......Page 342
14.4 Conclusion......Page 347
References......Page 348
Index......Page 352