Contents
Preface
1. Introduction of basic knowledge 1
1.1 Linear matrix inequalities 1
1.1.1 What are linear matrix inequalities? 1
1.1.2 Useful lemmas for linear matrix inequalities 8
1.1.3 Advantages of linear matrix inequalities 14
1.1.4 Some standard linear matrix inequalitie problems 15
1.2 Spacecraft attitude kinematics and dynamics 21
1.2.1 Attitude representations 22
1.2.2 Attitude kinematics 28
1.2.3 Attitude dynamics 31
References 34
2. State feedback nonfragile control 37
2.1 Introduction 37
2.2 Problem formulation 38
2.2.1 Attitude dynamics modeling 38
2.2.2 Control objective 42
2.3 State feedback nonfragile control law 43
2.3.1 Some lemmas 43
2.3.2 Sufficient conditions under additive perturbation 44
2.3.3 Sufficient conditions under multiplicative perturbation 48
2.4 Simulation test 50
2.4.1 Simulation results under additive perturbation 51
2.4.2 Simulation results under multiplicative perturbation 53
2.4.3 Simulation results using a mixed H2/HN controller 55
2.5 Conclusions 59
References 60
3. Dynamic output feedback nonfragile control 63
3.1 Introduction 63
3.2 Problem formulation 65
3.2.1 Attitude system description 65
3.2.2 Nonfragile control problem 68
3.2.3 Control objective 70
3.3 Dynamic output feedback nonfragile control law design 71
3.3.1 Some lemmas 71
3.3.2 Controller design under additive perturbation 76
3.3.3 Controller design under multiplicative perturbation 79
3.3.4 Controller design under coexisting additive and multiplicative perturbations 81
3.4 Simulation test 87
3.4.1 Simulation results under additive perturbation 87
3.4.2 Simulation results under multiplicative perturbation 93
3.4.3 Simulation results under coexisting additive and multiplicative perturbations 102
3.5 Conclusions 105
References 105
4. Observer-based fault tolerant delayed control 107
4.1 Introduction 107
4.2 Problem formulation 110
4.2.1 Attitude system description 110
4.2.2 Control objective 113
4.3 Observer-based fault tolerant control scheme 113
4.3.1 Intermediate observer design 113
4.3.2 Delayed controller design 114
4.3.3 Control solution 115
4.4 Simulation test 127
4.4.1 Simulation results using the proposed controller 128
4.4.2 Simulation results using the prediction-based sampled-dataHN controller 132
4.4.3 Comparison analysis using different controllers 134
4.5 Conclusions 136
References 136
5. Observer-based fault tolerant nonfragile control 139
5.1 Introduction 139
5.2 Problem formulation 142
5.2.1 Attitude system description 142
5.2.2 Stochastically intermediate observer design 146
5.2.3 Nonfragile controller design 147
5.2.4 Control objective 148
5.3 Feasible solution for both cases 148
5.3.1 Some lemmas 148
5.3.2 Sufficient conditions under additive perturbation 149
5.3.3 Sufficient conditions under multiplicative perturbation 152
5.4 Simulation test 156
5.4.1 Comparison analysis under additive perturbation 158
5.4.2 Comparison analysis under multiplicative perturbation 166
5.5 Conclusions 173
References 173
6. Disturbance observer-based controlwith input MRCs 177
6.1 Introduction 177
6.2 Problem formulation 180
6.2.1 Attitude system description 180
6.2.2 Control objective 182
6.3 Controller design and analysis 182
6.3.1 Some lemmas 183
6.3.2 Coexisting conditions for observer and controller gains 184
6.3.3 Proof and analysis 185
6.4 Simulation test 191
6.4.1 Nonzero angular rates 192
6.4.2 Zero angular rates 195
6.4.3 Evaluation indices for the three conditions 197
6.4.4 Parametric influence on control performance 200
6.5 Conclusions 202
References 203
7. Improved mixed H2/HN control with poles assignment constraint 205
7.1 Introduction 205
7.2 Problem formulation 208
7.2.1 Flexible spacecraft dynamics with two bending modes 208
7.2.2 HN and H2 performance constraint 209
7.2.3 Poles assignment 210
7.2.4 Control objective 211
7.3 Improved mixed H2/HN control law 211
7.3.1 Some lemmas 211
7.3.2 H2 control 213
7.3.3 Mixed H2/HN control 217
7.4 Simulation test 219
7.4.1 Simulation results using static output feedback controller 220
7.4.2 Simulation results using improved mixed H2/HN controller 222
7.4.3 Simulation results using a traditional mixed H2/HN controller 227
7.4.4 Comparison analysis using different controllers 230
7.5 Conclusions 230
References 231
8. Nonfragile HN controlwith input constraints 233
8.1 Introduction 233
8.2 Problem formulation 236
8.2.1 Attitude system description of flexible spacecraft 236
8.2.2 Passive and active vibration suppression cases 238
8.2.3 Brief introduction on piezoelectric actuators 240
8.2.4 Imp
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