Liapunov functions and stability in control theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Edition: | 2. ed., [softcover repr.] |
| Series: | Communications and control engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 235 S. graph. Darst. |
| ISBN: | 3642059686 9783642059681 |
Staff View
MARC
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| 245 | 1 | 0 | |a Liapunov functions and stability in control theory |c Andrea Bacciotti and Lionel Rosier |
| 250 | |a 2. ed., [softcover repr.] | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XIII, 235 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Communications and control engineering | |
| 650 | 7 | |a Controle (teoria de sistema e controle) |2 larpcal | |
| 650 | 7 | |a Estabilidade de liapunov |2 larpcal | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Lyapunov functions | |
| 650 | 4 | |a Stability | |
| 650 | 0 | 7 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |D s |
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| 700 | 1 | |a Rosier, Lionel |d 1967- |e Verfasser |0 (DE-588)12267393X |4 aut | |
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Record in the Search Index
| _version_ | 1804152924194996224 |
|---|---|
| adam_text | Contents
Preface
V
1
Differential equations
1
1.1
Recall about existence results
................... 2
1.2
Differential inclusions
....................... 4
1.3.1
The upper semi-continuous case
.............. 4
1.2.2
The Lipschitz continuous case
............... 8
1.3
Appendix
........................... . . . 13
2
Time invariant
systenas
19
2.1
The linear case
........................... 19
2.1.1
Stability
........................... 19
2.1.2
Internal stabilization
.................... 22
2.1.3
External stabilization
................... 23
2.1.4
Quadratic forms
...................... 24
2.2
Nonlinear systems: stability
.................... 27
2.2.1
Internal notions
....................... 27
2.2.2
Converse theorems
..................... 30
2.2.3
Generalized Liapunov functions
..,.,,..,.,,,, 37
2.2.4
Absolute stability
...................... 39
Я.Я.5
Stability and robustness
.................. 44
2.2.6
The
Invariance
Principle
.................. 47
Я.2.7
The domain, of attraction
................. 49
2.2.8
Comparison functions
........,,..,..,.,, öö
2.2.9
External notions
........,,.,....,..... 58
2.3
Nonlinear systems: stabilization
.................. 62
2.3.1
Necessary condition for internal stabilization
...... 63
2.3.2
Asymptotic controllability and local controllability
... 68
XII Contents
2.3.3 Affine
systems: internal stabilization
........... 70
2.3.4 Affine
systems: external stabilization
........... 77
2.4
Output systems
........................... 79
2.5
Cascade systems
.......................... 80
2.6
Appendix
.............................. 83
3
Time varying systems
89
3.1
Two examples
............................ 89
3.2
Reformulation of the basic definitions
.............. 94
3.2.1
Stability and attraction
.................. 94
3.2.2
Time dependent Liapunov functions
........... 101
3.3
Sufficient conditions
........................ 104
3.4
Converse theorems
......................... 105
3.4.1
Asymptotic stability
.................... 100
3.4.2
Uniform stability
...................... 105
3.5
Robust stabilitv
.......................... . 10
3.6 Lagrange
stability
......................... 112
3.7
Discontinuous right hand side
................... 113
3.8
Time varying feedback
....................... 113
4
Differential inclusions
119
4.1
Global asymptotic stability
.................... 119
4.1.1
Sufficient conditions
.................... 119
4.1.2
Time invariant systems
.................. 121
4.1.3
Time varying systems
................... 122
4.1.4
Proof of the converse of second Liapunov theorem
. . . 125
4.2
Robust stability
........................... 148
4.2.1
Sufficient conditions
.................... 148
4.2.2
Converse of first Liapunov theorem
............ 152
4.2.3
Proof of the converse of first Liapunov theorem
..... 153
4.2.4
Application to external stabilization
........... 160
4.3
Nonsmooth Liapunov functions
.................. 161
5
Additional properties of strict Liapunov functions
167
•5.1
Estimates for the convergence of trajectories
........... 170
5.1.1
Exponenti il
stability
.................... 170
5.1.2
Rational stability
...................... 171
5.1.3
Finite-time stability
.................... 175
5.2
Analyticity
............................. 176
Contents XIII
5.2.1
Analytic
unsolvability
of the stability
problem
..... 176
5.2.2
Analytic Liapunov functions
................ 177
5.2.3
Holomorphic systems
.................... 180
5.3
Weighted homogeneity
....................... 180
5.3.1
A few definitions
...................... 181
5.3.2
Homogeneous Liapunov functions
............. 183
5.3.3
Application to the stabilization problem
......... 186
5.4
Symmetries and Liapunov functions
............... 192
5.4.1
Discrete symmetry
..................... 193
5.4.2
Infinitesimal symmetry
................... 193
5.4.3
Symmetric Liapunov functions
.............. 196
β
jVionotonicity and. generalized derivatives
6.1
Tools from nonsmooth analysis
.................. 203
6.2
Functions of one variable
..........,,,..,...... 207
6.3
Ordinary differential equations
.................. 209
6.4
Differential inclusions
.....,.,,.,.,,...,.,.,. 212
6.5
Monotonicity
and the proximal gradient
,..,..,.,,... 215
Bibliography
ЙІ9
Index
233
List of Abbreviations
237
|
| any_adam_object | 1 |
| author | Bacciotti, Andrea 1948- Rosier, Lionel 1967- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 880 |
| ctrlnum | (OCoLC)903721358 (DE-599)BVBBV042323839 |
| dewey-full | 629.8/312 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.8/312 |
| dewey-search | 629.8/312 |
| dewey-sort | 3629.8 3312 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | 2. ed., [softcover repr.] |
| format | Book |
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| id | DE-604.BV042323839 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:18:26Z |
| institution | BVB |
| isbn | 3642059686 9783642059681 |
| language | German |
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| owner_facet | DE-739 |
| physical | XIII, 235 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Communications and control engineering |
| spelling | Bacciotti, Andrea 1948- Verfasser (DE-588)122673921 aut Liapunov functions and stability in control theory Andrea Bacciotti and Lionel Rosier 2. ed., [softcover repr.] Berlin [u.a.] Springer 2010 XIII, 235 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Communications and control engineering Controle (teoria de sistema e controle) larpcal Estabilidade de liapunov larpcal Control theory Lyapunov functions Stability Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s DE-604 Rosier, Lionel 1967- Verfasser (DE-588)12267393X aut 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=027760710&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bacciotti, Andrea 1948- Rosier, Lionel 1967- Liapunov functions and stability in control theory Controle (teoria de sistema e controle) larpcal Estabilidade de liapunov larpcal Control theory Lyapunov functions Stability Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4167992-1 (DE-588)4032317-1 |
| title | Liapunov functions and stability in control theory |
| title_auth | Liapunov functions and stability in control theory |
| title_exact_search | Liapunov functions and stability in control theory |
| title_full | Liapunov functions and stability in control theory Andrea Bacciotti and Lionel Rosier |
| title_fullStr | Liapunov functions and stability in control theory Andrea Bacciotti and Lionel Rosier |
| title_full_unstemmed | Liapunov functions and stability in control theory Andrea Bacciotti and Lionel Rosier |
| title_short | Liapunov functions and stability in control theory |
| title_sort | liapunov functions and stability in control theory |
| topic | Controle (teoria de sistema e controle) larpcal Estabilidade de liapunov larpcal Control theory Lyapunov functions Stability Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Controle (teoria de sistema e controle) Estabilidade de liapunov Control theory Lyapunov functions Stability Ljapunov-Stabilitätstheorie Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027760710&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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