Linear Port-Hamiltonian systems on infinite-dimensional spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel
Birkhäuser Verlag GmbH
2014
|
| Edition: | [softcover repr. of the hardcover 1. ed. 2012] |
| Series: | Operator theory
223 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XII, 217 S. graph. Darst. 235 mm x 155 mm, 361 g |
Staff View
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| 245 | 1 | 0 | |a Linear Port-Hamiltonian systems on infinite-dimensional spaces |c Birgit Jacob ; Hans J. Zwart |
| 250 | |a [softcover repr. of the hardcover 1. ed. 2012] | ||
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Record in the Search Index
| _version_ | 1804152865417068544 |
|---|---|
| adam_text | Contents
List of Figures
xi
1
Introduction I
1.1
Examples
................................ 1
1.2
How to control a system?
.......................
б
1.3
Exercises
................................ 10
1.4
Notes and references
.......................... 12
2
State Space Representation
їй
2.1
State space models
........................... 13
2.2
Solutions of the state space models
.................. 19
2.3
Port-Hamiltonian systems
....................... 21
2.4
Exercises
................................ 24
2.5
Notes and references
.......................... 25
3
Controllability of Finite-Dimensional Systems
27
3.1
Controllability
............................. 27
3.2
Normal forms
.............................. 33
3.3
Exercises
................................ 36
3.4
Notes and references
.......................... 38
4
Stabilizability of Finite-Dimensional Systems
39
4.1
Stability and stabilizability
...................... 39
4.2
The pole placement problem
...................... 40
4.3
Characterization of stabilizability
................... 44
4.4
Stabilization of
port-Hamiłtoman
systems
..,.,...,,,...
4.Y
4.5
Exercises
...................,..,.,,,..,,. 48
4.6
Notes and
référencée
................ = ......... 49
5
Strongly
Continuóos
Semigroups
Ы
5.1
Strongly continuous semigroups
.................... 51
5.2
Infinitesimal generators
........................ 57
t>4
VII
viii Contents
5.3
Abstract
differential equations
..................... 61
5.4
Exercises
................................ 62
5.5
Notes and references
.......................... 63
6
Contraction and Unitary Semigroups
65
6.1
Contraction semigroups
........................ 65
6.2
Groups and unitary groups
...................... 73
6.3
Exercises
................................ 75
6.4
Notes and references
.......................... 77
7
Homogeneous Port-Hamiltonian Systems
79
7.1
Port-Hamiltonian systems
....................... 79
7.2
Generation of contraction semigroups
................. 84
7.3
Technical lemmas
............................ 92
7.4
Exercises
................................ 93
7.5
Notes and references
.......................... 96
8
Stability
97
8.1
Exponential stability
.......................... 97
8.2
Spectral projection and invariant subspaces
............. 101
8.3
Exercises
................................ 108
8.4
Notes and references
.......................... 109
9
Stability of Port-Hamiltonian Systems 111
9.1
Exponential stability of port-Hamiltonian systems
.........
Ill
9.2
An example
............................... 118
9.3
Exercises
................................ 120
9.4
Notes and references
.......................... 122
10
Inhomogeneous Abstract Differential Equations and Stabilization
123
10.1
The abstract inhomogeneous Cauchy problem
............ 123
10.2
Outputs
................................. 130
10.3
Bounded perturbations of Co-semigroups
............... 132
10.4
Exponential stabilizability
....................... 133
10.5
Exercises
................................ 139
10.6
Notes and references
.......................... 140
11
Boundary Control Systems
143
11.1
Boundary control systems
...................... . 143
11.2
Outputs for boundary control systems
................ 147
11.3
Port-Hamiltonian systems as boundary control systems
...... 148
11.4
Exercises
............................... 154
11.5
Notes and references
.......................... 155
Contents
їх
12 Transfer
Functions
157
12.1 Basic
definition and properties
.................... 158
12.2
Transfer functions for port-Hamiltonian systems
.......... 163
12.3
Exercises
................................ 167
12.4
Notes and references
.......................... 169
13
Well-posedness
171
13.1
Well-posedness for boundary control systems
............ 171
13.2
Well-posedness for port-Hamiltonian sj^stems
............ 181
13.3
P{H diagonal
.............................. 186
13.4
Proof of Theorem
13.2.2........................ 189
13.5
Well-posedness of the vibrating string
................ 191
1.3.6
Exercises
................................ 193
13.7
Notes and references
.......................... 195
A Integration and Hardy Spaces
19 /
A.I Integration theory
........................... 197
A.
2
The Hardy spaces
............................ 202
Bibliography
МШ
Index Mb
Birgit Jacob and Hans J.
Zwart
Linear Port-Hamiltonian Systems
on Infinite-dimensional
Spaces
This book provides a self-contained introduction to the theory of infinite-dimensional
systems theory and its applications to port-Hamiltonian systems. The textbook starts
with elementary known results, then progresses smoothly to advanced topics in current
research.
Many physical systems can be formulated using a Hamiltonian framework, leading to
models described by ordinary or partial differential equations. For the purpose of control
and for the interconnection of two or more Hamiltonian systems it is essential to take
into account this interaction with the environment.
This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An
abstract functional analytical approach is combined with the physical approach to
Hamiltonian systems. This combined approach leads to easily verifiable conditions for
well-posedness and stability.
The book is accessible to graduate engineers and mathematicians with a minimal
background in functional analysis. Moreover, the theory is illustrated by many worked-
out examples.
|
| any_adam_object | 1 |
| author | Jacob, Birgit |
| author_GND | (DE-588)1065676085 |
| author_facet | Jacob, Birgit |
| author_role | aut |
| author_sort | Jacob, Birgit |
| author_variant | b j bj |
| building | Verbundindex |
| bvnumber | BV042293242 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)901220449 (DE-599)BVBBV042293242 |
| discipline | Mathematik |
| edition | [softcover repr. of the hardcover 1. ed. 2012] |
| format | Book |
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| indexdate | 2024-07-10T01:17:30Z |
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| language | English |
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| physical | XII, 217 S. graph. Darst. 235 mm x 155 mm, 361 g |
| publishDate | 2014 |
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| publisher | Birkhäuser Verlag GmbH |
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| series | Operator theory |
| series2 | Operator theory Linear operators and linear systems |
| spelling | Jacob, Birgit Verfasser (DE-588)1065676085 aut Linear Port-Hamiltonian systems on infinite-dimensional spaces Birgit Jacob ; Hans J. Zwart [softcover repr. of the hardcover 1. ed. 2012] Basel Birkhäuser Verlag GmbH 2014 XII, 217 S. graph. Darst. 235 mm x 155 mm, 361 g txt rdacontent n rdamedia nc rdacarrier Operator theory 223 Linear operators and linear systems distributed parameter systems Hamiltonian systems control theory strongly continuous semigroups Dimension unendlich (DE-588)4474010-4 gnd rswk-swf Systemtheorie (DE-588)4058812-9 gnd rswk-swf Hamilton-Formalismus (DE-588)4376155-0 gnd rswk-swf Hamilton-Gleichungen (DE-588)4289066-4 gnd rswk-swf Verallgemeinerung (DE-588)4316262-9 gnd rswk-swf Unendlichdimensionales System (DE-588)4207956-1 gnd rswk-swf Systemtheorie (DE-588)4058812-9 s Dimension unendlich (DE-588)4474010-4 s DE-604 Hamilton-Gleichungen (DE-588)4289066-4 s Verallgemeinerung (DE-588)4316262-9 s Unendlichdimensionales System (DE-588)4207956-1 s Hamilton-Formalismus (DE-588)4376155-0 s 1\p DE-604 Zwart, Hans J. Sonstige oth Operator theory 223 (DE-604)BV000000970 223 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=027730359&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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=027730359&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jacob, Birgit Linear Port-Hamiltonian systems on infinite-dimensional spaces Operator theory distributed parameter systems Hamiltonian systems control theory strongly continuous semigroups Dimension unendlich (DE-588)4474010-4 gnd Systemtheorie (DE-588)4058812-9 gnd Hamilton-Formalismus (DE-588)4376155-0 gnd Hamilton-Gleichungen (DE-588)4289066-4 gnd Verallgemeinerung (DE-588)4316262-9 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd |
| subject_GND | (DE-588)4474010-4 (DE-588)4058812-9 (DE-588)4376155-0 (DE-588)4289066-4 (DE-588)4316262-9 (DE-588)4207956-1 |
| title | Linear Port-Hamiltonian systems on infinite-dimensional spaces |
| title_auth | Linear Port-Hamiltonian systems on infinite-dimensional spaces |
| title_exact_search | Linear Port-Hamiltonian systems on infinite-dimensional spaces |
| title_full | Linear Port-Hamiltonian systems on infinite-dimensional spaces Birgit Jacob ; Hans J. Zwart |
| title_fullStr | Linear Port-Hamiltonian systems on infinite-dimensional spaces Birgit Jacob ; Hans J. Zwart |
| title_full_unstemmed | Linear Port-Hamiltonian systems on infinite-dimensional spaces Birgit Jacob ; Hans J. Zwart |
| title_short | Linear Port-Hamiltonian systems on infinite-dimensional spaces |
| title_sort | linear port hamiltonian systems on infinite dimensional spaces |
| topic | distributed parameter systems Hamiltonian systems control theory strongly continuous semigroups Dimension unendlich (DE-588)4474010-4 gnd Systemtheorie (DE-588)4058812-9 gnd Hamilton-Formalismus (DE-588)4376155-0 gnd Hamilton-Gleichungen (DE-588)4289066-4 gnd Verallgemeinerung (DE-588)4316262-9 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd |
| topic_facet | distributed parameter systems Hamiltonian systems control theory strongly continuous semigroups Dimension unendlich Systemtheorie Hamilton-Formalismus Hamilton-Gleichungen Verallgemeinerung Unendlichdimensionales System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027730359&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027730359&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
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