Introduction to infinite-dimensional systems theory: a state-space approach
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
Springer
[2020]
|
| Schriftenreihe: | Texts in applied mathematics
volume 71 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032709384&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xii, 752 Seiten Illustrationen |
| ISBN: | 9781071605882 |
Internformat
MARC
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| 490 | 1 | |a Texts in applied mathematics |v volume 71 | |
| 650 | 4 | |a Systems Theory, Control | |
| 650 | 4 | |a Control and Systems Theory | |
| 650 | 4 | |a System theory | |
| 650 | 4 | |a Control engineering | |
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Datensatz im Suchindex
| _version_ | 1819292911333801984 |
|---|---|
| adam_text | Contents 1 2 3 Preface.......................................................................................................... v Introduction................................................................................................ 1 1.1 Motivation......................................................................................... 1 1.2 Systems theory concepts in finite dimensions.............................. 7 1.3 Aims of this book............................................................................. 13 Semigroup Theory .................................................................................... 17 2.1 Strongly continuous semigroups...................................................... 17 2.2 Abstract differential equations................................... 40 2.3 Contraction and dual semigroups................................................... 45 2.4 Invariant subspaces........................................................................... 51 2.5 Exercises........................................................................ 59 2.6 Notes and references......................................................................... 70 Classes of Semigroups........................................................ 71 3.1 Spatially invariant semigroups........................................................ 71 3.2 Riesz-spectral operators.................................................................... 79 3.3 Delay equations................................................................................ 109 3.4 Characterization of invariant
subspaces........................................ 125 3.5 Exercises........................................................................................... 132 3.6 Notes and references......................................................................... 149 ix
x 4 5 6 7 Contents Stability......................................................................................................... 151 4.1 Exponential stability......................................................................... 151 4.2 Weak and strong stability............................................................... 164 4.3 Sylvester equations........................................................................... 171 4.4 Exercises........................................................................................... 176 4.5 Notes and references......................................................................... 185 The Cauchy Problem................................................................................ 187 5.1 The abstract Cauchy problem........................................................ 187 5.2 Asymptotic behaviour...................................................................... 199 5.3 Perturbations and composite systems............................................. 202 5.4 Exercises........................................................................................... 214 5.5 Notes and references......................................................................... 219 State Linear Systems.................................................................................. 221 6.1 Input and outputs............................................................................. 221 6.2 Controllability and observability.................................................... 224 6.3 Tests for controllability and observability in
infinite time......... 6.4 Input and output stability.................................................................. 264 6.5 Lyapunov equations......................................................................... 268 6.6 Exercises........................................................................................... 6.7 Notes and references......................................................................... 288 248 274 Input-Output Maps.................................................................................... 291 7.1 Impulse response............................................................................. 291 7.2 Transfer functions............................................................................. 295 7.3 Transfer functions and the Laplace transform of the impulse response.................................................................... 306 7.4 Input-output stability and system stability...................................... 310 7.5 Dissipativity and passivity................................................................ 320 7.6 Exercises............................................................................................ 328 7.7 Notes and references......................................................................... 341
Contents 8 9 xi Stabilizability and Detectability............................................................... 343 8.1 Exponential stabilizability and detectability ................................. 343 8.2 Tests for exponential stabilizability and detectability................... 8.3 Compensator design......................................................................... 364 8.4 Strong stabilizability......................................................................... 370 8.5 Exercises........................................................................................... 8.6 Notes and references......................................................................... 382 Linear Quadratic Optimal Control........................................................ 353 373 385 9.1 The problem on a finite-time interval............................................. 385 9.2 The problem on the infinite-time interval...................................... 408 9.3 System properties of the closed-loop system................................. 423 9.4 Maximal solution to the algebraic Riccatiequation...................... 9.5 Linear quadratic optimal control for systems 432 with nonzero feedthrough............................................................... 445 9.6 Exercises........................................................................................... 449 9.7 Notes and references......................................................................... 476 10 Boundary Control Systems...................................................................... 479 10.1
General formulation........................................................................ 479 10.2 Transfer functions............................................................................. 487 10.3 Flexible beams with two types of boundary control................... 491 10.4 Exercises........................................................................................... 503 10.5 Notes and references........................................................................ 521 11 Existence and Stability for Semilinear Differential Equations......... 523 11.1 Existence and uniqueness of solutions.......................................... 523 11.2 Lyapunov stability theory............................................................... 534 11.3 Semilinear differential equations with holomorphic Riesz-spectral generators................................................................. 566 11.4 Exercises........................................................................................... 591 11.5 Notes and references........................................................................ 606
xii Contents A Mathematical Background....................................................................... 609 A.l Complex analysis.............................................................................. 609 A.2 Normed linear spaces....................................................................... 616 A.2.1 General theory.................................................................... 616 A.2.2 Hilbert spaces...................................................................... 622 Operators on normed linear spaces.................................................. 628 A.3.1 General theory.................................................................... 628 A.3.2 Operators on Hilbert spaces............................................... 644 Spectral theory................................................................................... 660 A.4.1 General spectral theory...................................................... 660 A.4.2 Spectral theory for compact normal operators................. 667 A.3 A.4 A.5 A.6 A.7 Integration and differentiation theory............................................. 672 A.5.1 Measure theory.................................................................... 672 A.5.2 Integration theory............................................................... 673 A.5.3 Differentiation theory........................................................... 682 Frequency-domain spaces................................................................ 689 A.6.1 Laplace and Fourier transforms........................................ 689 A.6.2
Frequency-domain spaces.................................................. 693 A.6.3 The Hardy spaces................................................................ 696 A.6.4 Frequency-domain spaces on the unit disc..................... 702 Algebraic concepts............................................................................ 708 A.7.1 General definitions............................................................. 708 A.7.2 Coprirnefactorizations over principal ideal domains ... 713 A.7.3 Coprirne factorizations over commutative integral domains................................................................................ 719 A.7.4 The convolution algebras Ή(β)........................................ 720 References..................................................................................................... 727 Notation........................................................................................................ 739 Index 743
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| any_adam_object | 1 |
| author | Curtain, Ruth F. 1941- Zwart, Hans J. 1959- |
| author_GND | (DE-588)141409916 (DE-588)141521465 |
| author_facet | Curtain, Ruth F. 1941- Zwart, Hans J. 1959- |
| author_role | aut aut |
| author_sort | Curtain, Ruth F. 1941- |
| author_variant | r f c rf rfc h j z hj hjz |
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| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV047306344 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T19:15:41Z |
| institution | BVB |
| isbn | 9781071605882 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032709384 |
| oclc_num | 1192976541 |
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| owner_facet | DE-11 DE-83 DE-739 |
| physical | xii, 752 Seiten Illustrationen |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spellingShingle | Curtain, Ruth F. 1941- Zwart, Hans J. 1959- Introduction to infinite-dimensional systems theory a state-space approach Texts in applied mathematics Systems Theory, Control Control and Systems Theory System theory Control engineering Systemtheorie (DE-588)4058812-9 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd |
| subject_GND | (DE-588)4058812-9 (DE-588)4207956-1 (DE-588)4151278-9 |
| title | Introduction to infinite-dimensional systems theory a state-space approach |
| title_auth | Introduction to infinite-dimensional systems theory a state-space approach |
| title_exact_search | Introduction to infinite-dimensional systems theory a state-space approach |
| title_full | Introduction to infinite-dimensional systems theory a state-space approach Ruth Curtain ; Hans Zwart |
| title_fullStr | Introduction to infinite-dimensional systems theory a state-space approach Ruth Curtain ; Hans Zwart |
| title_full_unstemmed | Introduction to infinite-dimensional systems theory a state-space approach Ruth Curtain ; Hans Zwart |
| title_short | Introduction to infinite-dimensional systems theory |
| title_sort | introduction to infinite dimensional systems theory a state space approach |
| title_sub | a state-space approach |
| topic | Systems Theory, Control Control and Systems Theory System theory Control engineering Systemtheorie (DE-588)4058812-9 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd |
| topic_facet | Systems Theory, Control Control and Systems Theory System theory Control engineering Systemtheorie Unendlichdimensionales System Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032709384&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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