Linear Control Theory: The State Space Approach

Linear Control Theory: The State Space Approach......Page 4
Contents......Page 8
Preface......Page 14
1.2 Review of Second Order Systems......Page 16
1.3 Introduction to State Space Modeling......Page 22
1.4 Solving the State Differential Equation......Page 24
1.5 Coordinate Transformation......Page 27
1.6 Diagonalizing Coordinate Transformation......Page 30
1. 7 State Trajectories Revisited......Page 36
1.8 State Space Models for the Complete Response......Page 41
1.9 Diagonal Form State Model......Page 47
1.10 Computer Calculation of the State and Output......Page 52
1.11 Notes and References......Page 54
2.1 Introduction......Page 56
2.2 State Feedback......Page 57
2.3 Eigenvalue Assignment......Page 59
2.4 Controllability......Page 70
2.5 Controllable Decomposed Form......Page 75
2.6 Transformation to Controllable Decomposed Form......Page 79
2. 7 Notes and References......Page 81
3.1 Introduction......Page 82
3.2 Filtering for Stable Systems......Page 83
3.3 Observers......Page 84
3.4 Observer Design......Page 86
3.5 Observability......Page 90
3.6 Observable Decomposed Form......Page 93
3.7 Minimal Order Observer......Page 97
3.8 Notes and References......Page 105
4.2 Controllable-Observable Decomposition......Page 106
4.3 Introduction to the Observability Gramian......Page 109
4.4 Fundamental Properties of W0......Page 111
4.5 Introduction to the Controllability Gramian......Page 116
4.6 Balanced Realization......Page 119
4.7 The Lyapunov Equation......Page 122
4.8 Controllability Gramian Revisited......Page 126
4.9 Notes and References......Page 129
5.1 Introduction......Page 130
5.2 Observer Based Controllers......Page 131
5.3 Quadratic State Feedback Control......Page 134
5.4 Solving the QCARE......Page 142
5.5 Quadratic State Estimation......Page 152
5.6 Solving the QFARE......Page 158
5.8 Notes and References......Page 160
6.1 Introduction......Page 162
6.2 LQG State Feedback Control Problem......Page 164
6.3 LQG State Estimation Problem......Page 168
6.4 LQG Measured Output Feedback Problem......Page 172
6.5 Stabilizing Solution......Page 173
6. 7 Notes and References......Page 181
7.2 Time Domain Spaces......Page 182
7.3 Frequency Domain Hilbert Spaces......Page 188
7.4 The H00 Norm: SISO Systems......Page 196
7.5 The H00 Norm: MIMO Systems......Page 200
7.6 Summary......Page 205
7.7 Notes and References......Page 206
8.1 Introduction......Page 208
8.2 System Inversion......Page 211
8.3 Coprime Factorization......Page 216
8.4 State Models for Coprime Factorization......Page 221
8.5 Stabilizing Controllers......Page 228
8.6 Lossless Systems and Related Ideas......Page 234
8.8 Notes and References......Page 238
9.1 Introduction......Page 240
9.2 H00 State Feedback Control Problem......Page 242
9.3 H oo State Feedback Controller......Page 249
9.4 H 00 State Estimation Problem......Page 257
9.5 Sufficient Conditions......Page 260
9.7 Notes and References......Page 261
10.1 Introduction......Page 262
10.2 Development......Page 263
1 0.3 Hex Output Feedback Controllers......Page 269
10.4 H00 Separation Principle......Page 276
10.5 Summary......Page 284
10.6 Notes and References......Page 285
A.1 Multiple Eigenvalues and Controllability......Page 286
A.2 Block Upper Triangular Matrices......Page 287
A.3 Singular Value Decomposition (SVD)......Page 289
A.4 Different Forms for the SVD......Page 291
A.5 Matrix Inversion Lemma (MIL)......Page 292
Appendix 8: Reduced Order Model Stability......Page 294
C.1 Problems Relating to Chapter 1......Page 298
C.2 Problems Relating to Chapter 2......Page 300
C.3 Problems Relating to Chapter 3......Page 302
C.4 Problems Relating to Chapter 4......Page 303
C.5 Problems Relating to Chapter 5......Page 305
D.1 State Models and State Response......Page 308
D.2 Feedback and Controllability......Page 312
D.3 Observer Based Control Systems......Page 314
D.4 State Model Reduction......Page 318
References......Page 324
Index......Page 328