Analysis and design of descriptor linear systems:
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| Format: | Book |
| Language: | English |
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New York, NY
Springer
[2010]
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| Series: | Advances in mechanics and mathematics
23 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | xix, 494 Seiten Illustrationen |
| ISBN: | 9781441963963 |
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Titel: Analysis and design of descriptor linear systems
Autor: Duan, Guang-Ren
Jahr: 2010
Contents
Preface. vii
List of Notation. xvii
1 Introduction. 1
1.1 Models for Descriptor Systems. 1
1.1.1 State Space Representation. 1
1.1.2 Time-Invariant Descriptor Linear Systems. 3
1.2 Examples of Descriptor Linear Systems. 5
1.2.1 Electrical Circuit Systems. 5
1.2.2 Large-Scale Systems with Interconnections. 7
1.2.3 Constrained Mechanical Systems. 8
1.2.4 Robotic System-A Three-Link Planar Manipulator. 12
1.3 Problems for Descriptor Linear Systems Analysis and Design. 18
1.3.1 Feedback in Descriptor Linear Systems. 18
1.3.2 Problems for Descriptor Linear Systems Analysis. 22
1.3.3 Problems for Descriptor Linear Systems Design. 24
1.4 Overview of the Book. 28
1.5 Notes and References. 29
Part I Descriptor Linear Systems Analysis
2 Equivalence and Solutions of Descriptor Linear Systems. 35
2.1 Restricted System Equivalence. 35
2.1.1 The Definition . 36
2.1.2 Common Properties. 38
2.2 Canonical Equivalent Forms. 40
2.2.1 Dynamics Decomposition Form. 40
2.2.2 The Kronecker Form. 43
2.2.3 Canonical Equivalent Forms for Derivative Feedback. 44
2.3 Solutions of Descriptor Linear Systems. 50
2.3.1 System Decomposition Based on the
Kronecker Form. 50
2.3.2 Solution to the Basic Types of Equations . 51
2.4 Notes and References. 55
Regular Descriptor Linear Systems. 57
3.1 Regularity of Descriptor Linear Systems . 57
3.1.1 The Definition and Its Relation with Solutions. 57
3.1.2 Criteria for Regularity. 61
3.2 Equivalence of Regular Descriptor Linear Systems. 64
3.2.1 Standard Decomposition Form. 65
3.2.2 The Inverse Form . 70
3.3 Transfer Function Matrices. 72
3.3.1 TheDefinition. 73
3.3.2 Properties. 74
3.4 State Responses of Regular Descriptor Linear
Systems: Distributional Solutions. 75
3.4.1 Solutions of Slow and Fast Subsystems. 76
3.4.2 The Distributional Solutions. 80
3.4.3 Examples. 81
3.5 State Responses of Regular Descriptor Linear
Systems: Classical Solutions. 83
3.5.1 Consistency. 84
3.5.2 The Classical Solutions . 85
3.5.3 The Example. 88
3.6 Generalized Eigenvalues and Eigenvectors. 89
3.6.1 Finite Eigenvalues and Eigenvectors. 90
3.6.2 Infinite Eigenvalues and Eigenvectors. 95
3.7 Eigenstructure Decomposition with Relation to
Standard Decomposition. 98
3.7.1 Eigenstructure Decomposition. 98
3.7.2 Relation with Standard Decomposition. 102
3.7.3 The Deflating Subspaces. 103
3.8 Stability. 107
3.8.1 TheDefinition . 107
3.8.2 The Direct Criterion. 108
3.8.3 Criterion via Lyapunov Equation. 110
3.8.4 Examples. 1ll
3.9 Admissibility: Stability plus Impulse-Freeness. 113
3.9.1 TheDefinition . 113
3.9.2 The Criterion. 114
3.9.3 The Example. 117
3.10 Notes and References. 117
4 Controllability and Observability. 121
4.1 State Reachable Subsets. 121
4.1.1 TheDefinition . 122
4.1.2 Characterization of ^ [0] and^t. 124
4.1.3 Two Examples. 130
4.2 Controllability. 131
4.2.1 C-Controllability. 132
4.2.2 R-Controllability. 135
4.2.3 I-Controllability and S-Controllability. 136
4.3 Observability. 142
4.3.1 C-Observability. 143
4.3.2 R-Observability. 147
4.3.3 I-Observability and S-Observability. 148
4.4 The Dual Principle. 153
4.4.1 The Dual System . 153
4.4.2 The Dual Principle. 154
4.5 Direct Criteria. 156
4.5.1 C-Controllability and C-Observability. 157
4.5.2 R-Controllability and R-Observability . 160
4.5.3 I-Controllability and I-Observability. 161
4.5.4 S-Controllability and S-Observability. 165
4.6 Criteria Based on Equivalent Forms. 165
4.6.1 Criteria Based on the Dynamics
Decomposition Form. 165
4.6.2 Criteria Based on the Inverse Form. 168
4.6.3 Criteria Based on Equivalent Form
for Derivative Feedback. 173
4.7 System Decomposition. 177
4.7.1 The General Structural Decomposition. 178
4.7.2 Special Cases. 181
4.8 Transfer Function Matrix and Minimal Realization. 185
4.8.1 Transfer Function Matrix. 185
4.8.2 Minimal Realization. 187
4.9 Notes and References. 194
Part II Descriptor Linear Systems Design
5 Regularization of Descriptor Linear Systems. 199
5.1 Regularizability under P- (D-) Feedback. 199
5.1.1 Proportional Feedback. 199
5.1.2 Derivative Feedback. 203
5.2 Regularizability under P-D Feedback. 207
5.2.1 Problem Formulation. 207
5.2.2 Regularizability Conditions. 209
5.3 Regularizing Controllers. 212
5.3.1 Problem Formulation. 212
5.3.2 Preliminaries. 213
5.3.3 The Conclusion. 214
5.4 Proof of Theorem 5.7 . 218
5.4.1 Preliminary Results. 218
5.4.2 Proof of Theorem 5.7. 220
5.5 Notes and References. 224
6 Dynamical Order Assignment and Normalization. 227
6.1 Assignable Dynamical Orders. 227
6.1.1 Full-State Derivative Feedback. 228
6.1.2 Partial-State Derivative Feedback. 232
6.2 Dynamical Order Assignment via Full-State Derivative Feedback . 235
6.2.1 Problem Formulation. 236
6.2.2 Preliminary Results. 237
6.2.3 Solution to the Problem. 238
6.3 Dynamical Order Assignment via State Derivative
Feedback with Minimum Norm. 240
6.3.1 Problem Formulation. 240
6.3.2 A Preliminary Result. 241
6.3.3 Solution to the Problem. 243
6.4 Dynamical Order Assignment via Partial-State
Derivative Feedback . 247
6.4.1 Problem Formulation. 247
6.4.2 Preliminary Results. 248
6.4.3 Solution to the Problem. 251
6.4.4 The Example. 254
6.5 Normalization of Descriptor Linear Systems. 256
6.5.1 Normalizability. 256
6.5.2 Normalizing Controllers. 259
6.6 Notes and References. 262
7 Impulse Elimination. 265
7.1 The Impulse-Free Property. 265
7.1.1 Basic Criteria. 266
7.1.2 Criteria Based on Equivalent Forms. 268
7.2 Impulse Elimination by State Feedback. 272
7.2.1 Solution Based on Dynamics Decomposition Forms. 272
7.2.2 Solution Based on Standard Decomposition. 276
7.2.3 Solution Based on Canonical Equivalent
Form for Derivative Feedback. 279
7.3 Impulse Elimination by Output Feedback. 281
7.3.1 Problem Formulation. 281
7.3.2 TheSolution. .282
7.4 I-Controllablizability and I-Observablizability. 284
7.4.1 Basic Criterion. 285
7.4.2 Criteria Based on Equivalent Forms. 289
7.5 Impulsive Elimination by P-D Feedback. 293
7.5.1 MethodI . 294
7.5.2 Method II. 298
7.6 Notes and References. 302
8 Pole Assignment and Stabilization. 305
8.1 Pole Assignment by State Feedback. 305
8.1.1 Problems Formulation. 305
8.1.2 Pole Assignment under R-Controllability. 307
8.1.3 Pole Assignment under S-Controllability. 310
8.2 Pole Assignment by P-D Feedback. 315
8.2.1 Problem Formulation. 315
8.2.2 TheSolution. 315
8.3 Stabilizability and Detectability. 318
8.3.1 Stabilizability. 319
8.3.2 Detectability . 321
8.4 Stabilizing Controller Design. 324
8.4.1 Design Based on Standard Decomposition. 324
8.4.2 Design Based on Controllability Canonical Forms. 327
8.4.3 Design Based on Lyapunov Theory . 330
8.5 Notes and References. 333
9 Eigenstructure Assignment. 337
9.1 The Problem. 338
9.1.1 TheProblem. 339
9.1.2 Interpretations of Requirements. 340
9.1.3 Problem Decomposition. 344
9.2 The Parametric Solution. 345
9.2.1 Solution of Closed-Loop Eigenvectors. 345
9.2.2 Solution of the Gain Matrix A". 347
9.2.3 The Algorithm for Problem 9.1. 350
9.3 The Left Eigenvector Matrix. 352
9.3.1 Preliminaries. 352
9.3.2 The Parametric Expressions. 353
9.4 Response of the Closed-Loop System. 356
9.4.1 The Canonical Form for the Closed-Loop System. 356
9.4.2 The Closed-Loop Response. 358
9.5 An Example. 361
9.5.1 The General Solutions. 362
9.5.2 Special Solutions. 363
9.6 Notes and References. 365
10 Optimal Control. 369
10.1 Introduction. 369
10.2 Optimal Linear Quadratic State Regulation. 371
10.2.1 Problem Formulation. 371
10.2.2 The Conversion. 372
10.2.3 The Optimal Regulator. 375
10.2.4 An Illustrative Example. 377
10.3 Time-Optimal Control . 379
10.3.1 Problem Formulation. 379
10.3.2 Time-Optimal Controlpf the Slow and Fast Subsystems. 380
10.3.3 TheSolution. 382
10.4 Notes and References. 385
11 Observer Design. 389
11.1 Introduction. 389
11.1.1 State Observers. 390
11.1.2 Function Kx Observers. 391
11.2 Descriptor State Observers. 392
11.2.1 Existence Condition. 392
11.2.2 Design Methods . 394
11.3 Eigenstructure Assignment Design. 396
11.3.1 Eigenstructure Assignment Result. 397
11.3.2 The Algorithm and Example. 399
11.4 Observer Design with Disturbance Decoupling. 402
11.4.1 Problem Formulation. 403
11.4.2 Preliminaries. 403
11.4.3 Constraints for Disturbance Decoupling.406
11.4.4 The Example. 407
11.5 Normal Reduced-Order State Observers.409
11.5.1 Normal Rank£-Order State Observers.409
11.5.2 Normal-State Observers of Order n - m. 412
11.6 Normal Function Kx Observers.417
11.6.1 Conditions for Normal Function Kx Observers. 417
11.6.2 Parametric Design for Normal Function Observers.419
11.7 Notes and References.424
Part III Appendices
A Some Mathematical Results.429
A.l Delta Function $(•).429
A.2 Laplace Transform.432
A.3 Determinants and Inverses of Block Matrices.434
A.4 Nilpotent Matrices.437
A.5 Some Operations of Linear Subspaces.441
A.6 Kernels and Images of Matrices.443
A.7 Singular Value Decomposition.445
B Rank-Constrained Matrix Matching and Least Square Problems. 451
B. 1 The Problems. 451
B.2 Preliminaries. 452
B.3 Solution to Problem B.l . 455
B.4 Solution to Problem B.2 . 458
B.5 An Illustrative Example. 461
B.6 Proof of Lemma B.4 . 462
C Generalized Sylvester Matrix Equations. 465
C.l Introduction. 465
C.2 Preliminaries. 466
C.3 Solution Based on Right Coprime Factorization. 468
C.4 Solution Based on SVD. 472
C.5 An Example . 473
References. 477
Index.491 |
| any_adam_object | 1 |
| author | Duan, Guang-Ren |
| author_GND | (DE-588)1046927698 |
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| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.832 |
| dewey-search | 629.832 |
| dewey-sort | 3629.832 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Book |
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| isbn | 9781441963963 |
| language | English |
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| spelling | Duan, Guang-Ren (DE-588)1046927698 aut Analysis and design of descriptor linear systems Guang-Ren Duan New York, NY Springer [2010] © 2010 xix, 494 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Advances in mechanics and mathematics 23 Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd rswk-swf Systementwurf (DE-588)4261480-6 gnd rswk-swf Lineares System (DE-588)4125617-7 gnd rswk-swf Lineares System (DE-588)4125617-7 s Differential-algebraisches Gleichungssystem (DE-588)4229517-8 s Systementwurf (DE-588)4261480-6 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4419-6397-0 Advances in mechanics and mathematics 23 (DE-604)BV017903734 23 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3476484&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024533323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Duan, Guang-Ren Analysis and design of descriptor linear systems Advances in mechanics and mathematics Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Systementwurf (DE-588)4261480-6 gnd Lineares System (DE-588)4125617-7 gnd |
| subject_GND | (DE-588)4229517-8 (DE-588)4261480-6 (DE-588)4125617-7 |
| title | Analysis and design of descriptor linear systems |
| title_auth | Analysis and design of descriptor linear systems |
| title_exact_search | Analysis and design of descriptor linear systems |
| title_full | Analysis and design of descriptor linear systems Guang-Ren Duan |
| title_fullStr | Analysis and design of descriptor linear systems Guang-Ren Duan |
| title_full_unstemmed | Analysis and design of descriptor linear systems Guang-Ren Duan |
| title_short | Analysis and design of descriptor linear systems |
| title_sort | analysis and design of descriptor linear systems |
| topic | Differential-algebraisches Gleichungssystem (DE-588)4229517-8 gnd Systementwurf (DE-588)4261480-6 gnd Lineares System (DE-588)4125617-7 gnd |
| topic_facet | Differential-algebraisches Gleichungssystem Systementwurf Lineares System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3476484&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024533323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV017903734 |
| work_keys_str_mv | AT duanguangren analysisanddesignofdescriptorlinearsystems |