Table of Contents
0.1 Preface v
0.2 Acknowledgments ix
1 Introduction 1
1.1 Notations and Definitions 3
1.1.1 Notations 3
1.1.2 Definitions 5
1.2 Time-Delay Systems 8
1.3 Uncertain Time-Delay Systems 9
1.4 System Examples 11
1.4.1 Stream Water Quality 11
1.4.2 Vehicle Following Systems 12
1.4.3 Continuous Stirred Tank Reactors with Recycling 13
1.4.4 Power Systems 14
1.4.5 Some Biological Models 15
1.5 Discrete-Time Delay Systems 16
1.5.1 Example 1.1 17
1.5.2 Example 1.2 18
1.6 Outline of the Book 18
1.7 Notes and References 20
I Robust Control
2 Robust Stability 27
2.1 Stability Results of Time-Delay Systems 27
2.1.1 Stability Conditions of Continuous-Time Systems 28
2.1.2 Example 2.1 31
2.1.3 Example 2.2 34
2.1 A Stability Conditions of Discrete-Time Systems 35
2.1.5 Example 2.3 37
2.1.6 Example 2.4 41
2.2 Robust Stability of UTDS 42
2.2.1 Stability Conditions for Continuous-Time Systems 42
2.2.2 Example 2.5 44
2.2.3 Example 2.6 49
2.2.4 Example 2.7 49
2.2.5 Stability Conditions for Discrete-Time Systems 49
2.2.6 Example 2.8 53
2.3 Stability Tests Using H∞-norm 53
2.4 Stability of Time-Lag Systems 54
2.4.1 Example 2.9 58
2.5 Stability of Linear Neutral Systems 61
2.6 Stability of Multiple-Delay Systems 65
2.7 Stability Using Lyaprrnov-Razumikhin Theorem 68
2.7.1 Example 2.10 70
2.8 Stability Using Comparison Principle 71
2.9 Notes and References 74
3 Robust Stabilization 75
3.1 Introduction 75
3.2 Time-Delay Systems 76
3.2.1 Problem Description 76
3.2.2 State Feedback Synthesis 77
3.2.3 Two-Term Feedback Synthesis 85
3.2.4 Static Output Feedback Synthesis 89
3.2.5 Dynamic Output Feedback Synthesis 91
3.3 Simulation Examples 95
3.3.1 Example 3.1 95
3.3.2 Example 3.2 96
3.3.3 Example 3.3 97
3.3.4 Example 3.4 97
3.3.5 Example 3.5 98
3.3.6 Example 3.6 98
3.3.7 Example 3.7 99
3.3.8 Example 3.8 99
3.4 Uncertain Time-Delay Systems 99
3.4.1 Problem Statement and Definitions 100
3.4.2 Closed-Loop System Stability 101
3.5 Nominal Control Synthesis 103
3.5.1 Example 3.9 105
3.6 Uncertainty Structures 106
3.6.1 Control Synthesis for Matched Uncertainties 107
3.6.2 Example 3.10 109
3.6.3 Control Synthesis for Mismatched Uncertainties 111
3.6.4 Example 3.11 114
3.6.5 Control Synthesis for Norm-Bounded Uncertainties 115
3.6.6 Example 3.12 118
3.7 Notes and References 119
4 Robust H∞ Control 121
4.1 Linear Uncertain Systems 122
4.1.1 Problem Statement and Preliminaries 122
4.1.2 Robust H∞ Control 124
4.2 Nonlinear Systems 126
4.2.1 Problem Statement and Preliminaries 127
4.2.2 Robust H∞ - Performance Results 135
4.3 Discrete-Time Systems 137
4.3.1 Problem Description and Preliminaries 138
4.3.2 Robust Control 141
4.4 Multiple-Delay Systems 143
4.4.1 Problem Description 144
4.4.2 State Feedback H∞-Control 145
4.4.3 Example 4.1 152
4.4.4 Problem Description with Uncertainties 152
4.4.5 Example 4.2 157
4.5 Linear Neutral Systems 158
4.5.1 Robust Stabilization 159
4.5.2 Robust H∞ Performance 161
4.6 Notes and References 165
5 Guaranteed Cost Control 167
5.1 Continuous-Time Systems 167
5.1.1 Uncertain State-Delay Systems 167
5.1.2 Robust Performance Analysis I 168
5.1.3 Robust Performance Analysis II 173
5.1.4 Synthesis of Guaranteed Cost Control I 176
5.1.5 Synthesis of Guaranteed Cost Control II 180
5.2 Discrete-Time Systems 184
5.2.1 Problem Formulation 184
5.2.2 Robust Performance Analysis III 185
5.2.3 Synthesis of Guaranteed Cost Control III 190
5.3 Observer-Based Control 193
5.3.1 Problem Description 194
5.3.2 Closed-Loop System 195
5.3.3 Robust Performance Analysis IV 196
5.3.4 Synthesis of Observer-Based Control 200
5.3.5 A Computational Algorithm 205
5.3.6 Example 5.1 206
5.4 Notes and References 207
6 Passivity Analysis and Synthesis 209
6.1 Introduction 209
6.2 Continuous-Time Systems 210
6.2.1 A Class of Uncertain Systems 210
6.2.2 Conditions of Passivity: Delay-Independent Stability 211
6.2.3 Conditions of Passivity: Delay-Dependent Stability 213
6.2.4 μ-Parameterization 216
6.2.5 Observer-Based Control Synthesis 220
6.3 Discrete-Time Systems 223
6.3.1 A Class of Discrete-Delay Systems 223
6.3.2 Conditions of Passivity: Delay-Independent Stability 225
6.3.3 Conditions of Passivity: Delay-Dependent Stability 227
6.3.4 Parameterization 236
6.3.5 State-Feedback Control Synthesis 240
6.3.6 Output-Feedback Control Synthesis 242
6.4 Notes and References 245
7 Interconnected Systems 247
7.1 Introduction 247
7.2 Problem Statement and Definitions 248
7.2.1 Uncertainty Structures 248
7.3 Decentralized Robust Stabilization I 250
7.4 Decentralized Robust H∞ Performance 257
7.4.1 Example 7.1 263
7.5 Decentralized Robust Stabilization II 265
7.5.1 Problem Statement and Preliminaries 265
7.6 Decentralized Stabilizing Controller 268
7.6.1 Adjustment Procedure 273
7.6.2 Example 7.2 273
7.7 Notes and References 276
II Robust Filtering
8 Robust Kalman Filtering 303
8.1 Introduction 303
8.2 Continuous-Time Systems 304
8.2.1 System Description 304
8.2.2 Robust Filter Design 305
8.2.3 A Riccati Equation Approach 307
8.2.4 Steady-State Filter 311
8.2.5 Example 8.1 314
8.3 Discrete-Time Systems 315
8.3.1 Uncertain Discrete-Delay Systems 315
8.3.2 Robust Filter Design 316
8.3.3 A Riccati Equation Approach 319
8.3.4 Steady-State Filter 323
8.3.5 Example 8.2 326
8.4 Notes and References 326
9 Robust H∞ Filtering 331
9.1 Introduction 331
9.2 Linear Uncertain Systems 332
9.2.1 Problem Description and Preliminaries 332
9.2.2 Robust H∞ Filtering 334
9.2.3 Worst-Case Filter Design 339
9.3 Nonlinear Uncertain Systems 342
9.3.1 Problem Description and Assumptions 342
9.3.2 Robust H∞ Filtering Results 348
9.4 Linear Discrete-Time Systems 354
9.4.1 Problem Description 354
9.4.2 H∞-Estimation Results 357
9.5 Linear Parameter-Varying Systems 365
9.5.1 Discrete-Time Models 366
9.5.2 Affine Quadratic Stability 367
9.5.3 Robust H∞ Filtering 372
9.6 Simulation Example 377
9.6.1 Example 9.1 377
9.7 Notes and References 378
10 Interconnected Systems 379
10.1 Introduction 379
10.2 Problem Statement 380
10.3 H∞ Performance Analysis 384
10.4 Robust H∞ Filtering 388
10.5 Notes and References 392
A Some Facts from Matrix Theory 399
A.1 Schur Complements 399
A.2 Matrix Inversion Lemma 399
A.3 Bounded Real Lemma 400
A.3.1 Continuous-Time Systems 400
A.3.2 Discrete-Time Systems 400
B Some Algebraic Inequalities 401
B.1 Matrix-Type Inequalities 401
B.2 Vector- or Scalar-Type Inequalities 405
C Stability Theorems 407
C.1 Lyapunov-Razumikhin Theorem 407
C.2 Lyapunov-Krasovskii Theorem 408
D Positive Real Systems 409
E LMI Control Software 413
E.1 Example E.1 415
E.2 Example E.2 416
Index 419
