Linear time-varying systems: algebraic-analytic approach
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
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| Series: | Lecture notes in control and information sciences
410 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXV, 635 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642197260 |
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| 245 | 1 | 0 | |a Linear time-varying systems |b algebraic-analytic approach |c Henri Bourlès ; Bogdan Marinescu |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
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IMAGE 1
CONTENTS
PART I: MATHEMATICAL TOOLS 1 CATEGORIES, DIVISIBILITY AND GROUPS 3
1.1 INTRODUCTION 3
1.2 CATEGORIES 4
1.2.1 SETS 4
1.2.2 GENERAL NOTIONS ON CATEGORIES 6
1.2.3 FUNCTORS 10
1.2.4 ABELIAN CATEGORIES 17
1.3 MONOIDS 27
1.3.1 MONOIDS AND CANCELLATION MONOIDS 27
1.3.2 IDEALS A MONOID, AND OTHER NOTIONS 28
1.3.3 HOMOMORPHISMS; QUOTIENT MONOIDS 30
1.3.4 PRODUCTS OF MONOIDS 32
1.4 DIVISIBILITY 32
1.4.1 DIVISORS AND MULTIPLES 32
1.4.2 REGULAR ELEMENTS AND TOTAL DIVISIBILITY 34
1.4.3 CONICAL MONOIDS 35
1.4.4 FREE MONOIDS 36
1.5 ORDERED SETS AND LATTICES 36
1.5.1 POSETS 36
1.5.2 BOUNDS AND CHAINS 37
1.5.3 ASCENDING AND DESCENDING CHAIN CONDITIONS 39 1.5.4 LATTICES 41
1.5.5 FOUR THEOREMS IN MODULAR LATTICES 43
1.5.6 UNIQUE FACTORIZATION MONOIDS 46
1.6 GROUPS 48
1.6.1 GROUPS AND THEIR GENERATORS 48
1.6.2 SUBGROUPS 49
1.6.3 NORMAL SUBGROUPS AND QUOTIENT GROUPS 50
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009990241
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
1.6.4 INDUCED HOMOMORPHISM, AND ISOMORPHISM THEOREMS 51
1.6.5 SIMPLE GROUPS, AND CYCLIC GROUPS 53
1.6.6 THE LATTICE OF NORMAL SUBGROUPS 54
1.6.7 COMMUTATORS, AND DERIVED GROUP 56
1.6.8 SOLVABLE GROUPS 57
1.6.9 ACTION OF A GROUP ON A SET 58
1.7 DIGRESSION 1: TOPOLOGICAL VECTOR SPACES 58
1.7.1 TOPOLOGICAL VECTOR SPACES 58
1.7.2 LOCALLY CONVEX TOPOLOGICAL VECTOR SPACES 61
1.7.3 SPECIAL CLASSES OF TOPOLOGICAL VECTOR SPACES 63 1.8 DIGRESSION 2:
MANIFOLDS AND LIE GROUPS 69
1.8.1 LIE GROUPS 69
1.8.2 LIE ALGEBRA OF A LIE GROUP 73
1.8.3 THE UNIVERSAL ENVELOPING ALGEBRA, AND ITS CENTRE . . 75 1.9
DIGRESSION 3: HYPERFUNCTIONS 76
1.9.1 HYPERFUNCTIONS ON AN OPEN SUBSET OF THE REAL LINE 76
1.9.2 EXAMPLES OF HYPERFUNCTIONS 79
1.9.3 GENERAL HYPERFUNCTIONS 80
1.9.4 HYPERFUNCTIONS WHICH ARE NOT DISTRIBUTIONS 82
1.10 EXERCISES 83
1.11 NOTES 89
RINGS AND MODULES 91
2.1 INTRODUCTION 91
2.2 RINGS AND MODULES 93
2.2.1 RINGS, IDEALS AND DIVISION RINGS 93
2.2.2 MODULES AND ALGEBRAS 95
2.2.3 HOMOMORPHISMS AND QUOTIENTS 97
2.2.4 FREE MODULES AND VECTOR SPACES 100
2.2.5 DUALITY 106
2.2.6 CHANGE OF BASIS 110
2.2.7 TENSOR PRODUCTS 112
2.3 GENERALIZED DIFFERENTIAL RINGS 114
2.3.1 DIFFERENTIAL RINGS 114
2.3.2 DIFFERENCE RINGS 114
2.3.3 GENERAL DERIVATIONS 115
2.4 IDEALS IN RINGS 116
2.4.1 MAXIMAL IDEALS 116
2.4.2 LATTICES, AND PRODUCTS OF IDEALS 117
2.4.3 PRIME IDEALS, AND COMPLETELY PRIME IDEALS 118
2.4.4 ARTINIAN RINGS, NOETHERIAN RINGS, AND SEMISIMPLE RINGS 120
2.4.5 PRIME RINGS, AND SEMIPRIME RINGS 122
IMAGE 3
CONTENTS XIX
2.5 RINGS OF FRACTIONS 123
2.5.1 THE COMMUTATIVE CASE 123
2.5.2 THE NONCOMMUTATIVE CASE 125
2.5.3 ORE DOMAINS 127
2.5.4 MODULES OVER RINGS OF FRACTIONS 128
2.6 LOCAL RINGS 130
2.6.1 DEFINITION OF A LOCAL RING 130
2.6.2 CHARACTERIZATION OF A LOCAL RING; LOCAL HOMOMORPHISM 130
2.6.3 A-ADIC COMPLETION 131
2.7 SKEW POLYNOMIALS: ELEMENTARY PROPERTIES 131
2.7.1 POLYNOMIALS IN A CENTRAL INDETERMINATE 131
2.7.2 DIFFERENTIAL OPERATORS 133
2.7.3 DIFFERENCE OPERATORS 134
2.7.4 GENERAL SKEW POLYNOMIALS 134
2.7.5 SIMPLICITY OF SOME SKEW POLYNOMIAL RINGS 139 2.8 SKEW LAURENT
POLYNOMIALS, AND RATIONAL FUNCTIONS 140 2.8.1 SKEW LAURENT POLYNOMIALS
140
2.8.2 DIVISION RING OF SKEW RATIONAL FUNCTIONS 141
2.8.3 SIMPLICITY OF SOME SKEW LAURENT POLYNOMIAL RINGS 141
2.8.4 CROSSED PRODUCTS 141
2.9 RINGS OF POWER SERIES 146
2.9.1 FORMAL POWER SERIES 146
2.9.2 FORMAL SKEW LAURENT SERIES 149
2.10 SOME LINEAR GROUPS 150
2.10.1 LINEAR ALGEBRAIC GROUPS 150
2.10.2 ELEMENTARY MATRICES 154
2.10.3 ELEMENTARY OPERATIONS 154
2.10.4 REDUCTION OF A MATRIX TO AN EQUIVALENT DIAGONAL FORM 155
2.10.5 STRUCTURE OF GL N (K) AND OF E N (K) 155
2.11 DETERMINANTS 156
2.11.1 COMMUTATIVE CASE 156
2.11.2 NONCOMMUTATIVE CASE 158
2.11.3 INVARIANT BASIS NUMBER 162
2.12 RANK OF A MATRIX 163
2.12.1 OUTER RANK 163
2.12.2 INNER RANK 164
2.12.3 INVERTIBILITY, PRIMENESS, AND FULLNESS 167
2.13 SPECIFIC RINGS 168
2.13.1 GCD DOMAINS 168
2.13.2 UNIQUE FACTORIZATION DOMAINS 170
2.13.3 BEZOUT DOMAINS 172
2.13.4 DEDEKIND DOMAINS 174
IMAGE 4
XX CONTENTS
2.13.5 PRINCIPAL IDEAL DOMAINS 176
2.13.6 EUCLIDEAN DOMAINS 178
2.14 EXERCISES 181
2.15 NOTES 186
3 HOMOLOGICAL ALGEBRA 189
3.1 INTRODUCTION 189
3.2 PRESENTATIONS AND SIMILARITY 190
3.2.1 PRESENTATION OF A MODULE 190
3.2.2 COHERENT MODULES, AND COHERENT RINGS 193
3.2.3 THE MATRIX OF A MODULE 196
3.2.4 SIMILAR MATRICES 200
3.2.5 SIMILARITY OVER BEZOUT DOMAINS 202
3.3 CYCLIC MODULES 203
3.3.1 CYCLIC MODULES OVER A GENERAL RING 203
3.3.2 CYCLIC MODULES OVER PRINCIPAL IDEAL DOMAINS 207 3.4 FUNCTORS IN
CATEGORIES OF MODULES 211
3.4.1 G) AND HORN 211
3.4.2 RESTRICTION AND EXTENSION OF THE RING OF SCALARS . . . 215 3.4.3
RELATION BETWEEN KERNELS AND COKERNELS 219
3.5 HOMOLOGICAL PROPERTIES OF CERTAIN MODULES 224
3.5.1 PROTECTIVE MODULES 224
3.5.2 INJECTIVE MODULES 229
3.5.3 FLAT MODULES 235
3.5.4 RESOLUTIONS 239
3.5.5 DIMENSION 243
3.5.6 COGENERATORS 247
3.6 MODULES OVER SPECIFIC RINGS 251
3.6.1 MODULES OVER BEZOUT DOMAINS 251
3.6.2 MODULES OVER PRINCIPAL IDEAL DOMAINS 254
3.6.3 MODULES OVER DEDEKIND DOMAINS 258
3.7 COPRIME FACTORIZATIONS OF MATRICES 260
3.7.1 LEFT-COPRIME FACTORIZATIONS AND RIGHT-COPRIME FACTORIZATIONS 260
3.7.2 DOUBLY COPRIME FACTORIZATIONS 261
3.8 EXERCISES 262
3.9 NOTES 267
4 GALOIS THEORY AND SKEW POLYNOMIALS 269
4.1 INTRODUCTION 269
4.2 FIELD EXTENSIONS 269
4.2.1 ALGEBRAIC FIELD EXTENSIONS 269
4.2.2 GALOIS FIELD EXTENSIONS 276
4.3 SKEW POLYNOMIALS AND RELATED NOTIONS 280
4.3.1 SKEW POLYNOMIAL RINGS 280
IMAGE 5
CONTENTS XXI
4.3.2 PSEUDO-LINEAR TRANSFORMATIONS 282
4.3.3 JORDAN CANONICAL FORM 285
4.3.4 ROOTS OF A SKEW POLYNOMIAL 287
4.3.5 VANDERMONDE, WRONSKIAN, AND CASORATIAN MATRICES 292
4.3.6 SOLUTIONS OF DIFFERENTIAL OPERATORS 294
4.4 PICARD-VESSIOT EXTENSIONS 296
4.4.1 GENERAL NOTIONS 296
4.4.2 DIFFERENTIAL GALOIS THEORY 300
4.4.3 DIFFERENCE GALOIS THEORY 304
4.5 EXERCISES 305
4.6 NOTES 307
PART II: ALGEBRAIC THEORY OF LINEAR SYSTEMS
5 SYSTEMS AND BEHAVIORS: A GENERAL SETTING 311
5.1 INTRODUCTION 311
5.2 THE MODULE-THEORETIC SETTING 312
5.2.1 LINEAR SYSTEMS 312
5.2.2 BEHAVIORS 313
5.2.3 THE CONNECTION BETWEEN SYSTEMS AND BEHAVIORS . . . 314 5.2.4 THE
CATEGORICAL POINT OF VIEW 316
5.2.5 THE USE OF LARGE COGENERATORS 317
5.3 GENERALIZATION OF THE MODULE-THEORETIC SETTING 320
5.3.1 GENERALIZED SYSTEMS AND ASSOCIATED BEHAVIORS 320 5.3.2 FURTHER
STUDY OF COGENERATORS 321
5.4 EXAMPLES OF LINEAR SYSTEMS 324
5.4.1 LTI SYSTEMS 324
5.4.2 LTV SYSTEMS (1) 327
5.4.3 LTV SYSTEMS (2) 332
5.5 LINEAR SYSTEMS, BEHAVIORS, AND THEIR RELATIONS 334
5.5.1 RELATIONS BETWEEN BEHAVIORS 334
5.5.2 CONTROL SYSTEMS 339
5.5.3 STATE-SPACE SYSTEMS 344
5.6 STRUCTURAL PROPERTIES OF LINEAR SYSTEMS 345
5.6.1 CONTROLLABILITY 345
5.6.2 DUALITY 362
5.6.3 OBSERVABILITY 365
5.6.4 BICOPRIME FACTORIZATIONS 366
5.7 DIFFERENTIAL-DIFFERENCE SYSTEMS 368
5.7.1 INTRODUCTIVE EXAMPLES 368
5.7.2 THE CATEGORY OF TOPOLOGICAL MODULES 371
5.7.3 COGENERATORS FOR TOPOLOGICAL MODULES 373
5.7.4 DIFFERENTIAL SYSTEMS WITH LUMPED SHIFTS OVER LIE GROUPS 375
IMAGE 6
XXII CONTENTS
5.7.5 DIFFERENTIAL SYSTEMS WITH DISTRIBUTED SHIFTS OVER LIE GROUPS 383
5.8 EXERCISES * 389
5.9 NOTES 399
6 FINITE POLES AND ZEROS OF LTV SYSTEMS 403
6.1 INTRODUCTION 403
6.2 EXPONENTIAL STABILITY 404
6.3 ROOTS, FACTORS AND SOLUTIONS 405
6.3.1 LINEAR FACTORS 405
6.3.2 MULTIPLE FACTORS 408
6.4 FIELD EXTENSIONS FOR THE CONTINUOUS-TIME CASE 419 6.4.1 THE FIELD OF
FORMAL LAURENT SERIES 419
6.4.2 FACTORIZATION OF SKEW POLYNOMIALS 420
6.4.3 FUNDAMENTAL SETS OF ROOTS AND PICARD-VESSIOT EXTENSIONS 422
6.5 THE MODULE FRAMEWORK 424
6.5.1 MODULES AND FULL SETS OF ZEROS 424
6.5.2 MODULES AND POLES 425
6.5.3 POLES AND STABILITY 426
6.5.4 THE CASE OF LINEAR TIME-INVARIANT SYSTEMS 426 6.6 MODULES OF POLES
AND ZEROS 427
6.6.1 SYSTEM POLES 427
6.6.2 INVARIANT ZEROS 428
6.6.3 TRANSMISSION POLES AND ZEROS 429
6.6.4 HIDDEN MODES 434
6.6.5 RELATIONS BETWEEN POLES AND ZEROS 436
6.7 THE CASE OF DISCRETE-TIME SYSTEMS 443
6.7.1 FACTORS AND ROOTS IN THE GENERAL CASE 443
6.7.2 POLES AND ZEROS OF PERIODIC DISCRETE-TIME SYSTEMS 445
6.8 THE CASE OF STATE-SPACE CONTINUOUS-TIME PERIODIC SYSTEMS 447
6.9 EXERCISES 449
6.10 NOTES AND REFERENCES 451
7 STRUCTURE AT INFINITY AND IMPULSIVE BEHAVIORS 453
7.1 INTRODUCTION 453
7.2 STRUCTURE AT INFINITY 455
7.2.1 MATRICES OVER S 455
7.2.2 SMITH-MACMILLAN FORM AT INFINITY 457
7.2.3 MODULES OVER S 462
7.3 IMPULSIVE SYSTEMS AND BEHAVIORS 467
IMAGE 7
CONTENTS XXIII
7.3.1 TEMPORAL SYSTEMS 467
7.3.2 SIGNAL SPACES AND THEIR RELATIONS 468
7.3.3 IMPULSIVE BEHAVIOR 472
7.3.4 CAUSAL LAPLACE TRANSFORM AND ANTICAUSAL Z- TRANSFORM 476
7.3.5 TEMPORAL INTERCONNECTIONS 480
7.3.6 THE AXIOMATIC CHARACTERIZATION OF TEMPORAL SYSTEM 482
7.4 POLES AND ZEROS AT INFINITY 485
7.4.1 UNCONTROLLABLE POLES AT INFINITY 486
7.4.2 SYSTEM POLES AT INFINITY 486
7.4.3 HIDDEN MODES AT INFINITY 487
7.4.4 INVARIANT ZEROS AT INFINITY 489
7.4.5 SYSTEM ZEROS AT INFINITY 489
7.4.6 TRANSMISSION POLES AND TRANSMISSION ZEROS AT INFINITY 490
7.4.7 RELATIONS BETWEEN THE VARIOUS POLES AND ZEROS AT INFINITY 492
7.5 EXERCISES 494
7.6 NOTES 496
PART III: APPLICATIONS
8 ANALYSIS OF LTV SYSTEMS 499
8.1 INTRODUCTION 499
8.2 NEED OF TIME-VARYING MODELS 500
8.2.1 CURRENT-MODE CONTROL OF A CONVERTER 500
8.2.2 MODELING HIGHWAY VEHICLES WITH TIME-VARYING VELOCITY 501
8.2.3 POLYNOMIAL TIME-VARYING MODELS 504
8.3 ANALYSIS OF STRUCTURAL PROPERTIES 505
8.3.1 CONTROLLABILITY AND OBSERVABILITY ANALYSIS 505
8.3.2 STABILITY ANALYSIS 513
9 MODELING: CHOICE OF THE INPUT VARIABLES OF AN LTV SYSTEM 515
9.1 INTRODUCTION 515
9.2 CRITERIA FOR THE CHOICE OF THE INPUTS 516
9.3 GENERAL ALGORITHM 518
9.4 CONTROL MODEL OF AN ELECTRICAL CIRCUIT 519
9.5 NOTES AND REFERENCES 522
IMAGE 8
XXIV CONTENTS
10 OPEN-LOOP CONTROL BY MODEL-MATCHING 523
10.1 INTRODUCTION 523
10.2 FEEDFORWARD EXACT MODEL-MATCHING 523
10.2.1 PROBLEM FORMULATION 523
10.2.2 TRANSMISSION POLES AND ZEROS AT INFINITY OF COMPOSITE TRANSFER
MATRICES 525
10.2.3 EXISTENCE OF PROPER SOLUTIONS 527
10.2.4 PARAMETRIZATION OF THE CLASS OF PROPER SOLUTIONS 529 10.3
FEEDBACK EXACT MODEL-MATCHING 531
10.3.1 DYNAMIC OUTPUT FEEDBACK EMM 531
10.3.2 DYNAMIC STATE FEEDBACK EMM 532
10.4 OUTPUT DISTURBANCE DECOUPLING PROBLEM 533
10.5 SYSTEM DECOUPLING PROBLEM 534
10.5.1 NECESSARY AND SUFFICIENT CONDITION FOR BLOCK-DECOUPLING 535
10.5.2 PARAMETRIZATION OF THE SOLUTIONS 536
10.5.3 PROPER AND MINIMAL DELAY SOLUTIONS 537
10.6 CASE OF A FACTS IN A POWER SYSTEM 539
10.7 CASE OF A DC MOTOR 541
10.8 NOTES AND REFERENCES 542
11 CLOSED-LOOP CONTROL BY OUTPUT FEEDBACK POLE PLACEMENT 545
11.1 INTRODUCTION 545
11.2 CLOSED-LOOP TRANSFER MATRICES AND STABILITY 545
11.3 REGULATOR SYNTHESIS AND IMPLEMENTATION 549
11.3.1 POLE PLACEMENT 549
11.3.2 CANONICAL FORMS OF TRANSFER FUNCTIONS 549
11.3.3 REGULATOR IMPLEMENTATION 551
11.4 PARAMETRIZATION OF THE CLASS OF STABILIZING CONTROLLERS 553 11.5
TWO-INPUT REGULATORS 555
11.5.1 THE TWO-DEGREES-OF-FREEDOM (2DOF) CONTROL STRUCTURE 555
11.5.2 APPLICATION TO THE CONTROL OF A VARIABLE FLUX DC MOTOR 560
11.6 APPLICATION TO THE CONTROL OF NONLINEAR SYSTEMS 562 11.6.1
DIFFERENTIAL FIELD EXTENSIONS 562
11.6.2 NONLINEAR SYSTEMS 563
11.6.3 LINEARIZATION 565
11.6.4 TRAJECTORY PLANNING 567
11.6.5 FLATNESS-BASED TRAJECTORY TRACKING 570
11.6.6 TRAJECTORY TRACKING BY LTV CONTROL 574
11.6.7 CONNECTIONS AND DIFFERENCES WITH THE GAIN-SCHEDULING CONTROL 578
11.7 NOTES AND REFERENCES 579
IMAGE 9
CONTENTS XXV
PART IV: COMPLEMENTS
12 ANALYTIC THEORY OF LTV SYSTEMS 583
12.1 INTRODUCTION 583
12.2 SOLUTIONS AND TRAJECTORIES 583
12.3 PERIODIC SYSTEMS 585
12.4 STABILITY 586
12.4.1 STABILITY DEFINITIONS 586
12.4.2 LYAPUNOV'S DIRECT METHOD 588
12.4.3 LINEAR SYSTEMS 590
12.4.4 LYAPUNOV'S INDIRECT METHOD 596
12.5 POLES OF THE SYSTEM 599
12.5.1 LYAPUNOV TRANSFORMATIONS 599
12.5.2 REDUCTION OF A LINEAR SYSTEM TO A TRIANGULAR FORM 600
12.5.3 POLES AND STABILITY 601
12.6 EXERCISES 602
12.7 NOTES AND REFERENCES 603
REFERENCES 605
INDEX 623 |
| any_adam_object | 1 |
| author | Bourlès, Henri Marinescu, Bogdan |
| author_facet | Bourlès, Henri Marinescu, Bogdan |
| author_role | aut aut |
| author_sort | Bourlès, Henri |
| author_variant | h b hb b m bm |
| building | Verbundindex |
| bvnumber | BV037421238 |
| classification_rvk | SI 845 |
| ctrlnum | (OCoLC)724923409 (DE-599)DNB1009990241 |
| dewey-full | 515.642 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.642 |
| dewey-search | 515.642 |
| dewey-sort | 3515.642 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| id | DE-604.BV037421238 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T11:09:18Z |
| institution | BVB |
| isbn | 9783642197260 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022573496 |
| oclc_num | 724923409 |
| open_access_boolean | |
| owner | DE-83 DE-703 DE-706 DE-824 DE-29T |
| owner_facet | DE-83 DE-703 DE-706 DE-824 DE-29T |
| physical | XXV, 635 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Bourlès, Henri Verfasser aut Linear time-varying systems algebraic-analytic approach Henri Bourlès ; Bogdan Marinescu Berlin [u.a.] Springer 2011 XXV, 635 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 410 Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Zeitvariantes System (DE-588)4190654-8 gnd rswk-swf Algebraische Analysis (DE-588)4141832-3 gnd rswk-swf Lineares System (DE-588)4125617-7 gnd rswk-swf Zeitvariantes System (DE-588)4190654-8 s Lineares System (DE-588)4125617-7 s Algebraische Analysis (DE-588)4141832-3 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Marinescu, Bogdan Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-19727-7 Lecture notes in control and information sciences 410 (DE-604)BV005848579 410 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3669421&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022573496&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bourlès, Henri Marinescu, Bogdan Linear time-varying systems algebraic-analytic approach Lecture notes in control and information sciences Kontrolltheorie (DE-588)4032317-1 gnd Zeitvariantes System (DE-588)4190654-8 gnd Algebraische Analysis (DE-588)4141832-3 gnd Lineares System (DE-588)4125617-7 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4190654-8 (DE-588)4141832-3 (DE-588)4125617-7 |
| title | Linear time-varying systems algebraic-analytic approach |
| title_auth | Linear time-varying systems algebraic-analytic approach |
| title_exact_search | Linear time-varying systems algebraic-analytic approach |
| title_full | Linear time-varying systems algebraic-analytic approach Henri Bourlès ; Bogdan Marinescu |
| title_fullStr | Linear time-varying systems algebraic-analytic approach Henri Bourlès ; Bogdan Marinescu |
| title_full_unstemmed | Linear time-varying systems algebraic-analytic approach Henri Bourlès ; Bogdan Marinescu |
| title_short | Linear time-varying systems |
| title_sort | linear time varying systems algebraic analytic approach |
| title_sub | algebraic-analytic approach |
| topic | Kontrolltheorie (DE-588)4032317-1 gnd Zeitvariantes System (DE-588)4190654-8 gnd Algebraische Analysis (DE-588)4141832-3 gnd Lineares System (DE-588)4125617-7 gnd |
| topic_facet | Kontrolltheorie Zeitvariantes System Algebraische Analysis Lineares System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3669421&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=022573496&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005848579 |
| work_keys_str_mv | AT bourleshenri lineartimevaryingsystemsalgebraicanalyticapproach AT marinescubogdan lineartimevaryingsystemsalgebraicanalyticapproach |