Essentials of Robust Control

Cover......Page 0
Preface......Page 3
Contents......Page 7
Notation and Symbols......Page 11
Acronyms......Page 13
What is this book about?......Page 15
Highlights of this book......Page 17
Notes and References......Page 23
Problems......Page 24
Linear subspaces......Page 25
Eigenvalues and eigenvectors......Page 26
Matrix inversion formulas......Page 27
Invariant subspaces......Page 29
Vector norms and matrix norms......Page 30
Singular value decomposition......Page 33
Semidefinite matrices......Page 37
Problems......Page 38
Descriptions of linear dynamical systems......Page 41
Controllability and observability......Page 42
Observers and Observer-based controllers......Page 45
Operations on systems......Page 48
State-space realizations for transfer matrices......Page 49
Multivariable system poles and zeros......Page 52
Notes and references......Page 55
Problems......Page 56
Hilbert spaces......Page 59
H2 and H-infty spaces......Page 61
Computing L2 and H2 norms......Page 67
Computing L-infty and H-infty norms......Page 69
Notes and references......Page 75
Problems......Page 76
Feedback structure......Page 79
Well-posedness of feedback loop......Page 80
Internal stability......Page 82
Coprime factorization over RH-infty......Page 85
Problems......Page 91
Feedback properties......Page 95
Weighted H2 and H-infty performance......Page 99
Selection of weighting functions......Page 103
Bode's gain and phase relation......Page 108
Bode's sensitivity integral......Page 112
Analyticity constraints......Page 114
Problems......Page 116
7. Balanced Model Reduction......Page 119
Lyapunov equations......Page 120
Balanced realizations......Page 121
Model reduction by balanced truncation......Page 131
Frequency-weighted balanced model reduction......Page 138
Notes and references......Page 140
Problems......Page 141
Model uncertainty......Page 143
Small gain theorem......Page 151
Stability under unstructured uncertainties......Page 155
Robust performance......Page 161
Skewed specifications......Page 164
Classical control for MIMO systems......Page 168
Notes and references......Page 171
Problems......Page 172
Linear fractional transformations......Page 179
Basic principle......Page 187
Redheffer star products......Page 192
Notes and references......Page 194
Problems......Page 195
10. mu and mu Synthesis......Page 197
General framework for system robustness......Page 198
Structured singular value......Page 201
Structured robust stability and performance......Page 214
Overview of mu synthesis......Page 227
Notes and references......Page 230
Problems......Page 231
11. Controller Parameterization......Page 235
Existence of stabilizing controllers......Page 236
Parameterization of all stabilizing controllers......Page 238
Coprime factorization approach......Page 242
Problems......Page 245
12. Algebraic Riccati Equations......Page 247
Stabilizing solution and Riccati operator......Page 248
Inner functions......Page 259
Problems......Page 260
Introduction to regulator problem......Page 267
Standard LQR problem......Page 269
Extended LQR problem......Page 272
Guaranteed stability margins of LQR......Page 273
Standard H2 problem......Page 275
Stability margins of H2 controllers......Page 279
Problems......Page 281
Problem formulation......Page 283
A simplified H-infty control problem......Page 284
Optimality and limiting behavior......Page 296
an optimal controller......Page 300
General H-infty solutions......Page 302
Relaxing Assumptions......Page 305
H2 and H-infty integral control......Page 308
H-infty filtering......Page 311
Notes and references......Page 313
Problems......Page 314
15. Controller Reduction......Page 319
H-infty controller reductions......Page 320
Notes and references......Page 326
Problems......Page 327
Robust stabilization of coprime factors......Page 329
Loop-shaping design......Page 339
Justification for H-infty loop shaping......Page 342
Further guidelines for loop shaping......Page 348
Notes and references......Page 355
Problems......Page 356
17. Gap Metric and v-Gap Metric......Page 363
Gap metric......Page 364
v-Gap metric......Page 371
Geometric interpretationof v-gap metric......Page 384
Extended loop-shaping design......Page 387
Problems......Page 389
Model validation......Page 391
Mixed mu analysis and synthesis......Page 395
Notes and references......Page 403
Problems......Page 404
Bibliography......Page 405
Index......Page 421