The mathematics of networks of linear systems:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham ; Heidelberg ; New York ; Dordrecht ; London
Springer
2015
|
| Schriftenreihe: | Universitext
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028168363&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xiv, 662 Seiten Illustrationen |
| ISBN: | 9783319166452 |
| ISSN: | 0172-5939 |
Internformat
MARC
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| 100 | 1 | |a Fuhrmann, Paul Abraham |d 1937- |e Verfasser |0 (DE-588)141517077 |4 aut | |
| 245 | 1 | 0 | |a The mathematics of networks of linear systems |c Paul A. Fuhrmann ; Uwe Helmke |
| 264 | 1 | |a Cham ; Heidelberg ; New York ; Dordrecht ; London |b Springer |c 2015 | |
| 300 | |a xiv, 662 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext |x 0172-5939 | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Matrix theory | |
| 650 | 4 | |a Systems theory | |
| 650 | 4 | |a Linear and Multilinear Algebras, Matrix Theory | |
| 650 | 4 | |a Systems Theory, Control | |
| 650 | 4 | |a Control | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Systemtheorie |0 (DE-588)4058812-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Kontrolltheorie |0 (DE-588)4123657-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Kontrolltheorie |0 (DE-588)4123657-9 |D s |
| 689 | 0 | 1 | |a Systemtheorie |0 (DE-588)4058812-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Helmke, Uwe |d 1952-2016 |e Verfasser |0 (DE-588)172133122 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-319-16646-9 |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-028168363 | |
Datensatz im Suchindex
| _version_ | 1819305024454393856 |
|---|---|
| adam_text | Contents
1 Introduction ...................................................... 1
1.1 Control of Parallel Connections................................. 1
1.2 Synchronization of Coupled Harmonic Oscillators................. 6
1.3 Outline of the Book............................................ 13
Part I Algebraic Systems Theory: Foundations
2 Rings and Modules of Polynomials .................................... 23
2.1 Rings and Ideals............................................... 24
2.2 Divisibility and Coprimeness of Polynomials.................... 27
2.3 Modules........................................................ 36
2.4 Minimal Basis of Modules of Polynomials........................ 40
2.5 Divisibility and Coprimeness of Polynomial Matrices............ 45
2.6 Coprime Factorizations of Rational Matrix Functions............ 50
2.7 Wiener-Hopf Factorizations..................................... 55
2.8 Hermite and Smith Normal Forms ................................ 59
2.9 Equivalence of Polynomial Matrices............................. 63
2.10 Structure Theorem and Quotient Modules......................... 65
2.11 Rings of Rational Functions.................................... 70
2.12 Exercises...................................................... 79
2.13 Notes and References........................................... 82
3 Functional Models and Shift Spaces ................................ 85
3.1 Polynomial Models and the Shift Operator....................... 86
3.2 The Lattice of Shift-Invariant Subspaces....................... 91
3.3 Module Homomorphisms and Intertwining Maps................... 102
3.4 Classification of Shift Operators............................. 106
3.5 Rational Models............................................... 113
3.6 Duality..................................................... 122
3.7 The Matrix Chinese Remainder Theorem.......................... 126
3.8 Toeplitz Operators............................................ 128
XI
xii Contents
3.9 Exercises...................................................... 136
3.10 Notes and References........................................... 139
4 Linear Systems....................................................... 141
4.1 System Representations......................................... 142
4.2 Reachability and Observability................................. 151
4.3 Abstract Realization Theory.................................... 154
4.4 Equivalence of Realizations ................................... 161
4.5 The Shift Realization.......................................... 164
4.6 Strict System Equivalence...................................... 170
4.7 Poles and Zeros................................................ 178
4.8 Open-Loop Control ............................................. 188
4.9 Exercises...................................................... 201
4.10 Notes and References........................................... 204
Part II Algebraic Systems Theory: Advanced Topics
5 Tensor Products, Bezoutians, and Stability........................... 209
5.1 Tensor Products of Modules..................................... 211
5.2 Tensored Polynomial and Rational Models........................ 224
5.3 Polynomial Sylvester Equation.................................. 241
5.4 Generalized Bezoutians and Intertwining Maps................... 244
5.5 Stability Characterizations.................................... 256
5.6 Exercises...................................................... 276
5.7 Notes and References........................................... 278
6 State Feedback and Output Injection.................................. 281
6.1 State Feedback Equivalence..................................... 283
6.2 Polynomial Characterizations................................... 285
6.3 Reachability Indices and the Brunovsky Form ................... 291
6.4 Pole Assignment ............................................... 304
6.5 Rosenbrock’s Theorem........................................... 309
6.6 Stabilizability................................................ 312
6.7 Dynamic Output Feedback Stabilization.......................... 319
6.8 Controlled Invariant Subspaces................................. 331
6.9 Conditioned Invariant Subspaces................................ 341
6.10 Zeros and Geometric Control.................................... 347
6.11 Exercises...................................................... 349
6.12 Notes and References........................................... 351
7 Observer Theory ..................................................... 355
7.1 Classical State Observers...................................... 356
7.2 Observation Properties......................................... 360
7.3 Functional State Observers..................................... 373
7.4 Existence of Observers......................................... 384
7.5 Construction of Functional Observers........................... 398
Contents Al11
7.6 Exercises..................................................... 405
7.7 Notes and References.......................................... 406
Part III Networks of Linear Systems
8 Nonnegative Matrices and Graph Theory................................ 411
8.1 Nonnegative Matrices and Contractions ........................ 412
8.2 Perron—Frobenius Theorem...................................... 417
8.3 Stochastic Matrices and Markov Chains......................... 422
8.4 Graphs and Matrices........................................... 427
8.5 Graph Rigidity and Euclidean Distance Matrices ............... 434
8.6 Spectral Graph Theory......................................... 441
8.7 Laplacians of Simple Graphs................................... 450
8.8 Compressions and Extensions of Laplacians .................... 457
8.9 Exercises..................................................... 461
8.10 Notes and References.......................................... 464
9 Interconnected Systems............................................... 467
9.1 Interconnection Models...................................... 472
9.2 Equivalence of Interconnected Systems......................... 476
9.3 Reachability and Observability of Networks of Systems......... 484
9.4 Homogeneous Networks.......................................... 490
9.5 Special Coupling Structures................................... 492
9.6 Exercises..................................................... 502
9.7 Notes and References.......................................... 503
10 Control of Standard Interconnections................................. 507
10.1 Standard Interconnections..................................... 508
10.2 Open-Loop Controls for Parallel Connections................... 523
10.3 Open-Loop Control and Interpolation........................... 542
10.4 Exercises..................................................... 549
10.5 Notes and References.......................................... 551
11 Synchronization and Consensus........................................ 553
11.1 Consensus and Clustering in Opinion Dynamics.................. 554
11.2 Synchronization of Linear Networks............................ 566
11.3 Synchronization of Homogeneous Networks....................... 575
11.4 Polynomial Model Approach to Synchronization.................. 577
11.5 Examples: Arrays of Oscillators............................... 591
11.6 Exercises..................................................... 597
11.7 Notes and References.......................................... 598
12 Control of Ensembles ................................................ 601
12.1 Control of Parametric Families of Systems..................... 602
12.2 Uniform Ensemble Reachability................................. 605
12.3 Control of Platoons........................................... 617
xiv Contents
12.4 Control of Partial Differential Equations....................... 629
12.5 Exercises....................................................... 640
12.6 Notes and References............................................ 641
References................................................................. 645
Index...................................................................... 657
|
| any_adam_object | 1 |
| author | Fuhrmann, Paul Abraham 1937- Helmke, Uwe 1952-2016 |
| author_GND | (DE-588)141517077 (DE-588)172133122 |
| author_facet | Fuhrmann, Paul Abraham 1937- Helmke, Uwe 1952-2016 |
| author_role | aut aut |
| author_sort | Fuhrmann, Paul Abraham 1937- |
| author_variant | p a f pa paf u h uh |
| building | Verbundindex |
| bvnumber | BV042737431 |
| classification_rvk | SK 370 SK 880 |
| ctrlnum | (OCoLC)932081467 (DE-599)BVBBV042737431 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042737431 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T17:18:34Z |
| institution | BVB |
| isbn | 9783319166452 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028168363 |
| oclc_num | 932081467 |
| open_access_boolean | |
| owner | DE-11 DE-706 DE-20 DE-739 DE-188 DE-83 |
| owner_facet | DE-11 DE-706 DE-20 DE-739 DE-188 DE-83 |
| physical | xiv, 662 Seiten Illustrationen |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spellingShingle | Fuhrmann, Paul Abraham 1937- Helmke, Uwe 1952-2016 The mathematics of networks of linear systems Mathematics Matrix theory Systems theory Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Control Mathematik Systemtheorie (DE-588)4058812-9 gnd Lineare Kontrolltheorie (DE-588)4123657-9 gnd |
| subject_GND | (DE-588)4058812-9 (DE-588)4123657-9 |
| title | The mathematics of networks of linear systems |
| title_auth | The mathematics of networks of linear systems |
| title_exact_search | The mathematics of networks of linear systems |
| title_full | The mathematics of networks of linear systems Paul A. Fuhrmann ; Uwe Helmke |
| title_fullStr | The mathematics of networks of linear systems Paul A. Fuhrmann ; Uwe Helmke |
| title_full_unstemmed | The mathematics of networks of linear systems Paul A. Fuhrmann ; Uwe Helmke |
| title_short | The mathematics of networks of linear systems |
| title_sort | the mathematics of networks of linear systems |
| topic | Mathematics Matrix theory Systems theory Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Control Mathematik Systemtheorie (DE-588)4058812-9 gnd Lineare Kontrolltheorie (DE-588)4123657-9 gnd |
| topic_facet | Mathematics Matrix theory Systems theory Linear and Multilinear Algebras, Matrix Theory Systems Theory, Control Control Mathematik Systemtheorie Lineare Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028168363&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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