Introduction to infinite-dimensional systems theory: a state-space approach
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
[2020]
|
| Series: | Texts in applied mathematics
volume 71 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 752 Seiten Illustrationen |
| ISBN: | 9781071605882 |
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Record in the Search Index
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| 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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| adam_txt |
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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| spelling | Curtain, Ruth F. 1941- Verfasser (DE-588)141409916 aut Introduction to infinite-dimensional systems theory a state-space approach Ruth Curtain ; Hans Zwart New York, NY Springer [2020] © 2020 xii, 752 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics volume 71 Systems Theory, Control Control and Systems Theory System theory Control engineering Systemtheorie (DE-588)4058812-9 gnd rswk-swf Unendlichdimensionales System (DE-588)4207956-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Systemtheorie (DE-588)4058812-9 s Unendlichdimensionales System (DE-588)4207956-1 s DE-604 Zwart, Hans J. 1959- Verfasser (DE-588)141521465 aut Erscheint auch als Online-Ausgabe, pdf 978-1-07-160590-5 Texts in applied mathematics volume 71 (DE-604)BV002476038 71 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf 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 Inhaltsverzeichnis |
| 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_exact_search_txtP | 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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