System Theory (eBook)

Front Cover 1
System Theory: A Hilbert Space Approach 4
Copyright Page 5
Contents 8
Preface 12
Introduction 16
Part l: Operator Theory in Hilbert Resolution Space 20
Chapter 1. Causality 22
A. Hilbert Resolution Space 22
B. Causal Operators 25
C. Anticausal and Memoryless Operators 30
D. The Integrals of Triangular Truncation 33
E. Integral Representation 39
Problems 43
References 44
Chapter 2. Hypercausality 45
A. Strict Causality 45
B. Strong Strict Causality 52
C. Strong Causality 57
D. The Radical 60
Problems 65
References 66
Chapter 3. Decomposition 67
A. Decomposition in B 67
B. Decomposition in C 73
C. Decomposition in K 90
Problems 95
References 96
Chapter 4. Factorization 97
A. Regular Factorization 97
B. Radical Factorization 104
C. Compact Perturbations of the Identity 111
Problems 117
References 118
Chapter 5. Causal Invertibility 119
A. Sufficient Conditions 119
B. Topological Techniques 124
Problems 129
References 130
Notes for Part I 131
References 144
Part ll: State Space Theory 146
Chapter 6. State Models 148
A. State Decomposition 148
B. Controllability and Observability 152
C. Characterization Theory 160
Problems 163
References 164
Chapter 7. State Trajectory Factorization 165
A. State Trajectories 165
B. The State Trajectory Space 168
C. Lifting Theory 171
Problems 176
References 177
Notes for Part Il 178
References 184
Part III: Feedback Systems 186
Chapter 8. Feedback Models 188
A. Extension Spaces 188
B. Fractional Representation 195
C. Stability 205
D. Sensitivity 208
Problems 211
References 212
Chapter 9. Asymptotic Design 213
A. Stabilization 213
B. Tracking 219
C. Disturbance Rejection 223
Problems 227
References 228
Chapter 10. Optimal Control 229
A. A Basic Optimization Problem 229
B. The Servomechanism Problem 238
C. The Regulator Problem 243
Problems 246
References 247
Notes for Part lll 248
References 255
Part IV: Stochastic Systems 258
Chapter 11. Stochastic Optimization 260
A. Hilbert Space–Valued Random Variables 260
B. A Basic Stochastic Optimization Problem 267
C. Representation, Approximation, and Identification 274
Problems 276
References 276
Chapter 12. Estimation and Control 277
A. Filtering and Prediction 277
B. Open Loop Servomechanisms 280
C. Closed Loop Servomechanisms 284
D. Stochastic Regulators 288
Problems 294
References 294
Notes for Part IV 295
References 303
Selected Bibliography 306
Index 320
Pure and Applied Mathematics: A Series of Monographs and Textbooks 326