Hybrid dynamical systems: modeling, stability, and robustness
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton Univ Press
2012
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 212 S. graph. Darst. |
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| 100 | 1 | |a Goebel, Rafal |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Hybrid dynamical systems |b modeling, stability, and robustness |c Rafal Goebel, Ricardo G. Sanfelice and Andrew R. Teel |
| 264 | 1 | |a Princeton [u.a.] |b Princeton Univ Press |c 2012 | |
| 300 | |a XI, 212 S. |b graph. Darst. | ||
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| 700 | 1 | |a Teel, Andrew R. |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
ix
1
Introduction
1
1.1
The modeling framework
....................... 1
1.2
Examples in science and engineering
................ 2
1.3
Control system examples
....................... 7
1.4
Connections to other modeling frameworks
............ 15
1.5
Notes
................................. 22
2
The solution concept
25
2.1
Data of a hybrid system
....................... 25
2.2
Hybrid time domains and hybrid arcs
............... 26
2.3
Solutions and their basic properties
................. 29
2.4
Generators for classes of switching signals
............. 35
2.5
Notes
................................. 41
3
Uniform asymptotic stability, an initial treatment
43
3.1
Uniform global pre-asymptotic stability
.............. 43
3.2
Lyapunov functions
.......................... 50
3.3
Relaxed Lyapunov conditions
.................... 60
3.4
Stability from containment
..................... 64
3.5
Equivalent characterizations
..................... 68
3.6
Notes
................................. 71
4
Perturbations and generalized solutions
73
4.1
Differential and difference equations
................ 73
4.2
Systems with state perturbations
.................. 76
4.3
Generalized solutions
......................... 79
4.4
Measurement noise in feedback control
............... 84
4.5
Krasovskii solutions are Hermes solutions
............. 88
4.6
Notes
.................................
94
5
Preliminaries from set-valued analysis
97
5.1
Set convergence
............................ 97
5.2
Set-valued mappings
..............·..........
Wl
5.3
СгарЫса!
convergence of hybrid arcs
................ 107
vii
v{¡¡
CONTENTS
5.4
Differential inclusions
........................
Ш
5.5
Notes
................................. 115
Well-posed hybrid systems and their properties
117
6.1
Nominally well-posed hybrid systems
................ 117
6.2
Basic assumptions on the data
................... 120
6.3
Consequences of nominal well-posedness
.............. 125
6.4
Well-posed hybrid systems
...................... 132
6.5
Consequences of well-posedness
................... 134
6.6
Notes
................................. 137
Asymptotic stability, an in-depth treatment
139
7.1
Pre-asymptotic stability for nominally well-posed systems
.... 141
7.2
Robustness concepts
......................... 148
7.3
Well-posed systems
.......................... 151
7.4
Robustness corollaries
........................ 153
7.5
Smooth Lyapunov functions
..................... 156
7.6
Proof of robustness implies smooth Lyapunov functions
..... 161
7.7
Notes
................................. 167
Invariance
principles
169
8.1
Invariance
and
ω
-limits........................
169
8.2
Invariance
principles involving Lyapunov-like functions
...... 170
8.3
Stability analysis using
invariance
principles
............ 176
8.4
Meagre-limsup
invariance
principles
................ 178
8.5
Invariance
principles for switching systems
............. 181
8.6
Notes
................................. 184
Conical approximation and asymptotic stability
185
9.1
Homogeneous hybrid systems
.................... 185
9.2
Homogeneity and perturbations
................... 189
9.3
Conical approximation and stability
................ 192
9.4
Notes
................................. 196
Appendix; List of Symbols
199
Bibliography
201
Index
211
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:14:59Z |
| institution | BVB |
| language | English |
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| physical | XI, 212 S. graph. Darst. |
| publishDate | 2012 |
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| spelling | Goebel, Rafal Verfasser aut Hybrid dynamical systems modeling, stability, and robustness Rafal Goebel, Ricardo G. Sanfelice and Andrew R. Teel Princeton [u.a.] Princeton Univ Press 2012 XI, 212 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hybrides System (DE-588)4510314-8 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Hybrides System (DE-588)4510314-8 s Dynamisches System (DE-588)4013396-5 s DE-604 Sanfelice, Ricardo G. Verfasser aut Teel, Andrew R. Verfasser aut Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024816020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goebel, Rafal Sanfelice, Ricardo G. Teel, Andrew R. Hybrid dynamical systems modeling, stability, and robustness Hybrides System (DE-588)4510314-8 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4510314-8 (DE-588)4013396-5 |
| title | Hybrid dynamical systems modeling, stability, and robustness |
| title_auth | Hybrid dynamical systems modeling, stability, and robustness |
| title_exact_search | Hybrid dynamical systems modeling, stability, and robustness |
| title_full | Hybrid dynamical systems modeling, stability, and robustness Rafal Goebel, Ricardo G. Sanfelice and Andrew R. Teel |
| title_fullStr | Hybrid dynamical systems modeling, stability, and robustness Rafal Goebel, Ricardo G. Sanfelice and Andrew R. Teel |
| title_full_unstemmed | Hybrid dynamical systems modeling, stability, and robustness Rafal Goebel, Ricardo G. Sanfelice and Andrew R. Teel |
| title_short | Hybrid dynamical systems |
| title_sort | hybrid dynamical systems modeling stability and robustness |
| title_sub | modeling, stability, and robustness |
| topic | Hybrides System (DE-588)4510314-8 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Hybrides System Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024816020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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