Introduction to mathematical systems theory: a behavioral approach
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Springer
1998
|
| Schriftenreihe: | Texts in applied mathematics
26 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007881124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXIX, 424 S. Ill., graph. Darst. |
| ISBN: | 0387982663 |
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| adam_text | JAN WILLEM POLDERMAN JAN C. WILLEMS
INTRODUCTION TO MATHEMATICAL
SYSTEMS THEORY
A BEHAVIORAL APPROACH
WITH 89 ILLUSTRATIONS
SPRINGER
CONTENTS
SERIES PREFACE V
PREFACE VII
ACKNOWLEDGMENTS XIX
HOW TO USE THIS BOOK XXI
1 DYNAMICAL SYSTEMS 1
1.1 INTRODUCTION 1
1.2 MODELS 3
1.2.1 THE UNIVERSUM AND THE BEHAVIOR 3
1.2.2 BEHAVIORAL EQUATIONS 3
1.2.3 LATENT VARIABLES 5
1.3 DYNAMICAL SYSTEMS 8
1.3.1 THE BASIC CONCEPT 8
1.3.2 LATENT VARIABLES IN DYNAMICAL SYSTEMS 10
1.4 LINEARITY AND TIME-INVARIANCE 15
1.5 DYNAMICAL BEHAVIORAL EQUATIONS 16
1.6 RECAPITULATION 18
XXIV CONTENTS
1.7 NOTES AND REFERENCES 19
1.8 EXERCISES 19
2 SYSTEMS DEFINED BY LINEAR DIFFERENTIAL EQUATIONS 27
2.1 INTRODUCTION 27
2.2 NOTATION 28
2.3 CONSTANT-COEFFICIENT DIFFERENTIAL EQUATIONS 31
2.3.1 LINEAR CONSTANT-COEFFICIENT DIFFERENTIAL EQUATIONS 31
2.3.2 WEAK SOLUTIONS OF DIFFERENTIAL EQUATIONS 33
2.4 BEHAVIORS DEFINED BY DIFFERENTIAL EQUATIONS 37
2.4.1 TOPOLOGICAL PROPERTIES OF THE BEHAVIOR 37
2.4.2 LINEARITY AND TIME-INVARIANCE 42
2.5 THE CALCULUS OF EQUATIONS 43
2.5.1 POLYNOMIAL RINGS AND POLYNOMIAL MATRICES 43
2.5.2 EQUIVALENT REPRESENTATIONS 45
2.5.3 ELEMENTARY ROW OPERATIONS AND UNIMODULAR POLYNOMIAL
MATRICES 48
2.5.4 THE BEZOUT IDENTITY 51
2.5.5 LEFT AND RIGHT UNIMODULAR TRANSFORMATIONS 54
2.5.6 MINIMAL AND FULL ROW RANK REPRESENTATIONS 56
2.6 RECAPITULATION 59
2.7 NOTES AND REFERENCES 59
2.8 EXERCISES 60
2.8.1 ANALYTICAL PROBLEMS 62
2.8.2 ALGEBRAIC PROBLEMS 63
3 TIME DOMAIN DESCRIPTION OF LINEAR SYSTEMS 65
3.1 INTRODUCTION 65
3.2 AUTONOMOUS SYSTEMS 66
3.2.1 THE SCALAR CASE 68
3.2.2 THE MULTIVARIABLE CASE 76
3.3 SYSTEMS IN INPUT/OUTPUT FORM 80
3.4 SYSTEMS DEFINED BY AN INPUT/OUTPUT MAP 94
3.5 RELATION BETWEEN DIFFERENTIAL SYSTEMS AND CONVOLUTION SYSTEMS 96
3.6 WHEN ARE TWO REPRESENTATIONS EQUIVALENT? 99
3.7 RECAPITULATION 102
.3.8 NOTES AND REFERENCES 103
3.9 EXERCISES 103
CONTENTS XXV
STATE SPACE MODELS 115
4.1 INTRODUCTION 115
4.2 DIFFERENTIAL SYSTEMS WITH LATENT VARIABLES 116
4.3 STATE SPACE MODELS 116
4.4 INPUT/STATE/OUTPUT MODELS 121
4.5 THE BEHAVIOR OF I/S/O MODELS 123
4.5.1 THE ZERO INPUT CASE 123
4.5.2 THE NONZERO INPUT CASE: THE VARIATION OF THE CONSTANTS FOR-
MULA 125
4.5.3 THE INPUT/STATE/OUTPUT BEHAVIOR 126
4.5.4 HOW TO CALCULATE E
A
128
4.5.4.1 VIA THE JORDAN FORM 130
4.5.4.2 USING THE THEORY OF AUTONOMOUS BEHAVIORS ... 133
4.5.4.3 USING THE PARTIAL FRACTION EXPANSION OF (/ * A)
1
136
4.6 STATE SPACE TRANSFORMATIONS 138
4.7 LINEARIZATION OF NONLINEAR I/S/O SYSTEMS 139
4.8 RECAPITULATION 144
4.9 NOTES AND REFERENCES 144
4.10 EXERCISES 144
CONTROLLABILITY AND OBSERVABILITY 151
5.1 INTRODUCTION 151
5.2 CONTROLLABILITY 152
5.2.1 CONTROLLABILITY OF INPUT/STATE/OUTPUT SYSTEMS 164
5.2.1.1 CONTROLLABILITY OF I/S SYSTEMS 164
5.2.1.2 CONTROLLABILITY OF I/S/O SYSTEMS 170
5.2.2 STABILIZABILITY 171
5.3 OBSERVABILITY 173
5.3.1 OBSERVABILITY OF I/S/O SYSTEMS 177
5.3.2 DETECTABILITY 182
5.4 THE KALMAN DECOMPOSITION 184
5.5 POLYNOMIAL TESTS FOR CONTROLLABILITY AND OBSERVABILITY 187
5.6 RECAPITULATION 188
5.7 NOTES AND REFERENCES 189
5.8 EXERCISES 190
XXVI CONTENTS
6 ELIMINATION OF LATENT VARIABLES AND STATE SPACE REPRESENTATIONS 201
6.1 INTRODUCTION 201
6.2 ELIMINATION OF LATENT VARIABLES 202
6.2.1 MODELING FROM FIRST PRINCIPLES 202
6.2.2 ELIMINATION PROCEDURE 206
6.2.3 ELIMINATION OF LATENT VARIABLES IN INTERCONNECTIONS . . . .210
6.3 ELIMINATION OF STATE VARIABLES 211
6.4 FROM I/O TO I/S/O MODEL 215
6.4.1 THE OBSERVER CANONICAL FORM 216
6.4.2 THE CONTROLLER CANONICAL FORM 220
6.5 CANONICAL FORMS AND MINIMAL STATE SPACE REPRESENTATIONS .... 224
6.5.1 CANONICAL FORMS 225
6.5.2 EQUIVALENT STATE REPRESENTATIONS 226
6.5.3 MINIMAL STATE SPACE REPRESENTATIONS 228
6.6 IMAGE REPRESENTATIONS 228
6.7 RECAPITULATION 230
6.8 NOTES AND REFERENCES 231
6.9 EXERCISES 231
7 STABILITY THEORY 241
7.1 INTRODUCTION 241
7.2 STABILITY OF AUTONOMOUS SYSTEMS 244
7.3 THE ROUTH-HURWITZ CONDITIONS 247
7.3.1 THE ROUTH TEST 248
7.3.2 THE HURWITZ TEST 250
7.4 THE LYAPUNOV EQUATION 253
7.5 STABILITY BY LINEARIZATION 261
7.6 INPUT/OUTPUT STABILITY 265
7.7 RECAPITULATION 269
7.8 NOTES AND REFERENCES 270
7.9 EXERCISES 270
8 TIME- AND FREQUENCY-DOMAIN CHARACTERISTICS OF
LINEAR TIME-INVARIANT SYSTEMS 281
8.1 INTRODUCTION 281
8.2 THE TRANSFER FUNCTION AND THE FREQUENCY RESPONSE 282
8.2.1 CONVOLUTION SYSTEMS 283
CONTENTS XXVII
8.2.2 DIFFERENTIAL SYSTEMS 285
8.2.3 THE TRANSFER FUNCTION REPRESENTS THE CONTROLLABLE PART OF
THE BEHAVIOR 289
8.2.4 THE TRANSFER FUNCTION OF INTERCONNECTED SYSTEMS 289
8.3 TIME-DOMAIN CHARACTERISTICS 290
8.4 FREQUENCY-DOMAIN RESPONSE CHARACTERISTICS 294
8.4.1 THE BODE PLOT 295
8.4.2 THE NYQUIST PLOT 297
8.5 FIRST- AND SECOND-ORDER SYSTEMS 297
8.5.1 FIRST-ORDER SYSTEMS 297
8.5.2 SECOND-ORDER SYSTEMS 298
8.6 RATIONAL TRANSFER FUNCTIONS 300
8.6.1 POLE/ZERO DIAGRAM 301
8.6.2 THE TRANSFER FUNCTION OF I/S/O REPRESENTATIONS 301
8.6.3 THE BODE PLOT OF RATIONAL TRANSFER FUNCTIONS 303
8.7 RECAPITULATION 305
8.8 NOTES AND REFERENCES 306
8.9 EXERCISES 306
9 POLE PLACEMENT BY STATE FEEDBACK 311
9.1 OPEN LOOP AND FEEDBACK CONTROL 311
9.2 LINEAR STATE FEEDBACK 317
9.3 THE POLE PLACEMENT PROBLEM . 318
9.4 PROOF OF THE POLE PLACEMENT THEOREM 319
9.4.1 SYSTEM SIMILARITY AND POLE PLACEMENT 319
9.4.2 CONTROLLABILITY IS NECESSARY FOR POLE PLACEMENT 320
9.4.3 POLE PLACEMENT FOR CONTROLLABLE SINGLE-INPUT SYSTEMS . . .321
9.4.4 POLE PLACEMENT FOR CONTROLLABLE MULTI-INPUT SYSTEMS.... 322
9.5 ALGORITHMS FOR POLE PLACEMENT 324
9.6 STABILIZATION 327
9.7 STABILIZATION OF NONLINEAR SYSTEMS 328
9.8 RECAPITULATION 332
9.9 NOTES AND REFERENCES 333
9.10 EXERCISES 333
10 OBSERVERS AND DYNAMIC COMPENSATORS 341
10.1 INTRODUCTION 341
XXVIII CONTENTS
10.2 STATE OBSERVERS 344
10.3 POLE PLACEMENT IN OBSERVERS 346
10.4 UNOBSERVABLE SYSTEMS 348
10.5 FEEDBACK COMPENSATORS 350
10.6 REDUCED ORDER OBSERVERS AND COMPENSATORS 357
10.7 STABILIZATION OF NONLINEAR SYSTEMS 362
10.8 CONTROL IN A BEHAVIORAL SETTING 363
10.8.1 MOTIVATION 363
10.8.2 CONTROL AS INTERCONNECTION 366
10.8.3 POLE PLACEMENT 368
10.8.4 AN ALGORITHM FOR POLE PLACEMENT 370
10.9 RECAPITULATION 375
LO.LONOTES AND REFERENCES 375
10.11 EXERCISES 376
A SIMULATION EXERCISES 383
A.I STABILIZATION OF A CART 383
A.2 TEMPERATURE CONTROL OF A CONTAINER 385
A.3 AUTONOMOUS DYNAMICS OF COUPLED MASSES 388
A.4 SATELLITE DYNAMICS 389
A.4.1 MOTIVATION 389
A. 4.2 MATHEMATICAL MODELING 390
A. 4.3 EQUILIBRIUM ANALYSIS 392
A. 4.4 LINEARIZATION 393
A.4.5 ANALYSIS OF THE MODEL 393
A.4.6 SIMULATION 393
A.5 DYNAMICS OF A MOTORBIKE 394
A.6 STABILIZATION OF A DOUBLE PENDULUM 395
A.6.1 MODELING 395
A.6.2 LINEARIZATION 397
A.6.3 ANALYSIS 398
A.6.4 STABILIZATION 399
A.7 NOTES AND REFERENCES 400
B BACKGROUND MATERIAL 401
B.I POLYNOMIAL MATRICES 401
B.2 PARTIAL FRACTION EXPANSION 406
CONTENTS XXIX
B.3 FOURIER AND LAPLACE TRANSFORMS 408
B.3.1 FOURIER TRANSFORM 409
B.3.2 LAPLACE TRANSFORM 411
B.4 NOTES AND REFERENCES 411
B.5 EXERCISES 411
NOTATION 413
REFERENCES 415
INDEX 419
|
| any_adam_object | 1 |
| author | Polderman, Jan Willem 1956- Willems, Jan C. 1939- |
| author_GND | (DE-588)114680418 (DE-588)141941723 |
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| dewey-search | 003.8501135 |
| dewey-sort | 13.8501135 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
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| id | DE-604.BV011688696 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:16:57Z |
| institution | BVB |
| isbn | 0387982663 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007881124 |
| oclc_num | 246571297 |
| open_access_boolean | |
| owner | DE-20 DE-29T DE-384 DE-739 DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-706 DE-634 DE-83 DE-188 |
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| physical | XXIX, 424 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spellingShingle | Polderman, Jan Willem 1956- Willems, Jan C. 1939- Introduction to mathematical systems theory a behavioral approach Texts in applied mathematics Lineares zeitinvariantes System (DE-588)4213494-8 gnd Kontrolltheorie (DE-588)4032317-1 gnd Systemtheorie (DE-588)4058812-9 gnd |
| subject_GND | (DE-588)4213494-8 (DE-588)4032317-1 (DE-588)4058812-9 |
| title | Introduction to mathematical systems theory a behavioral approach |
| title_auth | Introduction to mathematical systems theory a behavioral approach |
| title_exact_search | Introduction to mathematical systems theory a behavioral approach |
| title_full | Introduction to mathematical systems theory a behavioral approach Jan Willem Polderman ; Jan C. Willems |
| title_fullStr | Introduction to mathematical systems theory a behavioral approach Jan Willem Polderman ; Jan C. Willems |
| title_full_unstemmed | Introduction to mathematical systems theory a behavioral approach Jan Willem Polderman ; Jan C. Willems |
| title_short | Introduction to mathematical systems theory |
| title_sort | introduction to mathematical systems theory a behavioral approach |
| title_sub | a behavioral approach |
| topic | Lineares zeitinvariantes System (DE-588)4213494-8 gnd Kontrolltheorie (DE-588)4032317-1 gnd Systemtheorie (DE-588)4058812-9 gnd |
| topic_facet | Lineares zeitinvariantes System Kontrolltheorie Systemtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007881124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT poldermanjanwillem introductiontomathematicalsystemstheoryabehavioralapproach AT willemsjanc introductiontomathematicalsystemstheoryabehavioralapproach |
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