Linear control systems: 1 Analysis of multivariable systems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Taunton
Research Studies Press u.a.
1992
|
| Schriftenreihe: | Industrial control, computers and communications series
6 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 379 S. |
| ISBN: | 0863801269 0471934283 |
Internformat
MARC
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| 264 | 1 | |a Taunton |b Research Studies Press u.a. |c 1992 | |
| 300 | |a XIX, 379 S. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | xiii
Contents
Symbols and Abbreviations
CHAPTER 1. GENERALISED LINEAR SYSTEMS 1
1.1 Generalised Continuous Time Systems 1
1.2 Generalised Discrete Time Systems 4
1.3 Solvability of Generalised Linear Systems 6
1.3.1 Solvability of generalised continuous time systems 6
1.3.2 Solvability of generalised discrete time systems 10
1.4 Determination of Solutions to Singular Linear Systems 16
1.4.1 Continuous time systems 16
1.4.2 Discrete time systems 23
1.5 Reduction of the Singular System to its Canonical Form 26
1.6 Impulsive Solutions to Singular Linear Systems 33
1.7 Transfer Matrices and Matrix Fraction Descriptions 35
1.7.1 Transfer matrices 35
1.7.2 Matrix fraction descriptions 39
1.7.3 Matrix fraction description of systems described by
state equations 45
1.7.4 Properness of transfer matrices 50
1.8 McMillan Form of Transfer Matrices 52
1.9 Description of Linear Dynamic Systems by Differential
(Difference) Operators and Their Transfer Matrices 56
1.10 System Matrices and Their Equivalence 58
1.10.1 System matrices 58
1.10.2 Equivalence and similarity of system matrices 60
Problems 64
References 66
xiv
CHAPTER 2. REACHABILITY, CONTROLLABILITY,
OBSERVABnJTYANDCONSTRUCTmUJTY 68
2.1 Reachability of Linear Regular Discrete Time Systems 68
2.2 Controllability of Linear Regular Discrete Time Systems 73
2.3 Observability of Linear Regular Discrete Time Systems 76
2.4 Constructibility of Linear Regular Discrete Time Systems 81
2.5 Reachability of Linear Regular Continuous Time Systems 82
2.6 Controllability of Linear Regular Continuous Time
Systems 85
2.7 Observability of Linear Regular Continuous Time Systems 86
2.8 Constructibility of Linear Regular Continuous Time
Systems 87
2.9 Output Reachability of Linear Regular Systems 88
2.10 Reachability and Observability of Linear Regular Systems
with State Feedback and Output Feedback 91
2.11 Reachability and Observability of Composite Linear
Systems 94
2.11.1 Systems connected in series 94
2.11.2 Systems connected in parallel 96
2.11.3 Systems with feedbacks 98
2.12 Reachability and Observability of Linear Systems Described
by Differential Operators 100
2.13 Reachability and Observability of Linear Composite
Systems Described by Differential Operators 104
2.13.1 Systems connected in series 104
2.13.2 Systems connected in parallel 105
2.13.3 Systems with feedbacks 106
2.14 Output Reachability of Linear Composite Systems 107
2.14.1 Systems connected in series 107
2.14.2 Systems connected in parallel 109
2.14.3 Systems with feedbacks 109
2.15 Controllability of Linear Singular Systems 110
2.15.1 Basic notions and R controllability 110
2.15.2 C controllability of linear singular systems 114
2.15.3 Impulse controllability of linear singular systems 116
2.15.4 Controllability at infinity and strong controllability
of linear singular systems 120
2.15.5 Relations among different types of controllability 125
2.16 Observability of Linear Singular Systems 126
2.16.1 Observability of a singular system with omitted
impulse part of its solution 126
2.16.2 Observability of subsystem S2 128
XV
2.16.3 Impulse observability of singular systems 130
2.16.4 Observability at infinity and strong observability
of singular systems 131
2.16.5 C observability and relations among different
types of observability 134
Problems 135
References 137
CHAPTER 3. CANONICAL FORMS FOR LINEAR
MULTIVARIABLE SYSTEMS 138
3.1 Linear Transformations 138
3.2 Canonical Forms for Single Input Single Output Systems 141
3.2.1 Single input systems 141
3.2.2 Single output systems 144
3.3 Canonical Forms for Multivariable Systems 146
3.3.1 Multi input systems 146
3.3.2 Multi output systems 163
3.4 Canonical Forms for Uncontrollable and Unobservable
Linear Systems 166
3.4.1 Uncontrollable multi input systems 166
3.4.2 Unobservable multi output systems 169
3.4.3 Kalman s canonical structure theorem 170
3.5 Canonical Forms for Generalised Linear Systems 174
Problems 178
References 179
CHAPTER 4. REALISATIONS OF TRANSFER MATRICES 181
4.1 Basic Definitions and Problem Formulation 181
4.2 Existence and Determination of Minimal Realisations 183
4.2.1 Some properties of minimal realisations 183
4.2.2 Determination of minimal realisations 186
4.2.2.1 Single input single output systems 186
4.2.2.2 Multi input single output systems 197
4.2.2.3 Single input multi output systems 199
4.2.2.4 Multi input multi output systems 200
4.3 Realisation Problem for Linear Systems Described by
Differential Operators 216
4.4 Realisation in the Weierstrass Canonical Form 219
4.5 Realisation of Generalised Linear Systems via Markov
Parameters 225
4.5.1 Problem formulation 225
xvi
4.5.2 Problem solution 226
Problems 234
References 236
CHAPTER 5. POLES AND ZEROS 238
5.1 Poles and Zeros of Transfer Matrices 238
5.1.1 Single input single output systems 238
5.1.2 Multi input multi output systems 239
5.2 Poles and Zeros of Linear Systems 248
5.2.1 Poles of the system 248
5.2.2 System zeros and invariant zeros 250
5.2.3 Input decoupling zeros 255
5.2.4 Output decoupling zeros 258
5.2.5 Input output decoupling zeros 261
5.2.6 Blocking zeros 263
5.3 Relationships between Poles and Zeros of Transfer
Matrices and Systems 264
5.3.1 Relationships between system poles, transmission
poles and decoupling zeros 264
5.3.2 Relationships between various types of zeros 266
5.4 Invariance of Zeros under Output Feedback 269
5.5 Infinite Poles and Zeros 273
5.5.1 Infinite poles and zeros of the transfer matrix 273
5.5.2 Infinite poles and zeros of the system 276
Problems 285
References 286
APPENDIX A 287
Regular Pencil of Matrices 287
Singular Pencil of Matrices 289
Kronecker s Indices of the Singular Pencil 296
System of Linear Differential Equations 299
Solution of Singular Systems of Linear Differential Equations by
Use of the Drazin Inverse 302
The Drazin inverse of square matrices 302
Computation of the Drazin inverse 307
System of Differential Equations 312
System of Difference Equations 317
Problems 318
References 318
xvii
APPENDIX B. POLYNOMIAL MATRICES 320
1. Basic Notions of Polynomial Matrices 320
2. Elementary Operations and Equivalent Polynomial
Matrices 323
3. Smith Canonical Form of Polynomial Matrices 329
4. Greatest Common Divisors and Least Common Multiples
of Polynomial Matrices 332
5. Generalised Bezout Identity 339
6. Similarity and Equivalence of Matrices 340
7. Tests for Coprimeness of Polynomial Matrices 342
8. Division of Polynomial Matrices 344
Problems 350
References 351
APPENDIX C. LINEAR SPACES AND MAPS 352
1. Linear Spaces 352
2. Linear Subspaces 356
3. Factor Spaces 361
4. Maps 364
5. Insertion, Restriction and Projection 369
6. Morphisms 370
7. Dual Spaces 371
8. Invariant Subspaces 374
Problems 375
References 376
Index 377
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:22:01Z |
| institution | BVB |
| isbn | 0863801269 0471934283 |
| language | English |
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| physical | XIX, 379 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Research Studies Press u.a. |
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| series | Industrial control, computers and communications series |
| series2 | Industrial control, computers and communications series |
| spelling | Kaczorek, Tadeusz 1932- Verfasser (DE-588)110868889 aut Linear control systems 1 Analysis of multivariable systems T. Kaczorek Taunton Research Studies Press u.a. 1992 XIX, 379 S. txt rdacontent n rdamedia nc rdacarrier Industrial control, computers and communications series 6 Industrial control, computers and communications series ... (DE-604)BV008622571 1 Industrial control, computers and communications series 6 (DE-604)BV000645478 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005670013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaczorek, Tadeusz 1932- Linear control systems Industrial control, computers and communications series |
| title | Linear control systems |
| title_auth | Linear control systems |
| title_exact_search | Linear control systems |
| title_full | Linear control systems 1 Analysis of multivariable systems T. Kaczorek |
| title_fullStr | Linear control systems 1 Analysis of multivariable systems T. Kaczorek |
| title_full_unstemmed | Linear control systems 1 Analysis of multivariable systems T. Kaczorek |
| title_short | Linear control systems |
| title_sort | linear control systems analysis of multivariable systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005670013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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