Liapunov functions and stability in control theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong
Springer
2001
|
| Series: | Lecture notes in control and information sciences
267 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 208 S. graph. Darst. |
| ISBN: | 1852334193 |
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MARC
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| 245 | 1 | 0 | |a Liapunov functions and stability in control theory |c Andrea Bacciotti and Lionel Rosier |
| 264 | 1 | |a London ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong |b Springer |c 2001 | |
| 300 | |a XI, 208 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in control and information sciences |v 267 | |
| 650 | 7 | |a Commande, Théorie de la |2 ram | |
| 650 | 7 | |a Liapounov, Fonctions de |2 ram | |
| 650 | 7 | |a Stabilité |2 ram | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Lyapunov functions | |
| 650 | 4 | |a Stability | |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kontrolltheorie |0 (DE-588)4032317-1 |D s |
| 689 | 0 | 1 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Rosier, Lionel |d 1967- |e Verfasser |0 (DE-588)12267393X |4 aut | |
| 830 | 0 | |a Lecture notes in control and information sciences |v 267 |w (DE-604)BV005848579 |9 267 | |
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Record in the Search Index
| _version_ | 1807229246128521216 |
|---|---|
| adam_text |
CONTENTS
1
DIFFERENTIAL
EQUATIONS
1
1.1
RECALL
ABOUT
EXISTENCE
RESULTS
.
2
1.2
DIFFERENTIAL
INCLUSIONS
.
4
1.2.1
THE
UPPER
SEMI-CONTINUOUS
CASE
.
4
1.2.2
THE
LIPSCHITZ
CONTINUOUS
CASE
.
8
1.3
APPENDIX
.
13
2
TIME
INVARIANT
SYSTEMS
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
.
26
2.2.1
INTERNAL
NOTIONS
.
27
2.2.2
CONVERSE
THEOREMS
.
30
2.2.3
GENERALIZED
LIAPUNOV
FUNCTIONS
.
36
2.2.4
ABSOLUTE
STABILITY
.
38
2.2.5
STABILITY
AND
ROBUSTNESS
.
43
2.2.6
COMPARISON
FUNCTIONS
.
46
2.2.7
EXTERNAL
NOTIONS
.
47
2.3
NONLINEAR
SYSTEMS:
STABILIZATION
.
52
2.3.1
NECESSARY
CONDITION
FOR
INTERNAL
STABILIZATION
.
53
2.3.2
ASYMPTOTIC
CONTROLLABILITY
AND
LOCAL
CONTROLLABILITY
.
57
2.3.3
AFFINE
SYSTEMS:
INTERNAL
STABILIZATION
.
60
2.3.4
AFFINE
SYSTEMS:
EXTERNAL
STABILIZATION
.
65
X
2.4
OUTPUT
SYSTEMS
.
67
2.5
CASCADE
SYSTEMS
.
68
3
TIME
VARYING
SYSTEMS
73
3.1
TWO
EXAMPLES
.
73
3.2
REFORMULATION
OF
THE
BASIC
DEFINITIONS
.
78
3.2.1
STABILITY
AND
ATTRACTION
.
78
3.2.2
TIME
DEPENDENT
LIAPUNOV
FUNCTIONS
.
84
3.3
SUFFICIENT
CONDITIONS
.
86
3.4
CONVERSE
THEOREMS
.
87
3.4.1
ASYMPTOTIC
STABILITY
.
87
3.4.2
UNIFORM
STABILITY
.
88
3.5
ROBUST
STABILITY
.
90
3.6
LAGRANGE
STABILITY
.
94
3.7
DISCONTINUOUS
RIGHT
HAND
SIDE
.
95
3.8
TIME
VARYING
FEEDBACK
.
96
4
DIFFERENTIAL
INCLUSIONS
101
4.1
GLOBAL
ASYMPTOTIC
STABILITY
.
101
4.1.1
SUFFICIENT
CONDITIONS
.
101
4.1.2
TIME
INVARIANT
SYSTEMS
.
103
4.1.3
TIME
VARYING
SYSTEMS
.
104
4.1.4
PROOF
OF
THE
CONVERSE
OF
SECOND
LIAPUNOV
THEOREM
.
.
.
107
4.2
ROBUST
STABILITY
.
130
4.2.1
SUFFICIENT
CONDITIONS
.
130
4.2.2
CONVERSE
OF
FIRST
LIAPUNOV
THEOREM
.
134
4.2.3
PROOF
OF
THE
CONVERSE
OF
FIRST
LIAPUNOV
THEOREM
.
135
4.2.4
APPLICATION
TO
EXTERNAL
STABILIZATION
.
142
5
ADDITIONAL
PROPERTIES
OF
STRICT
LIAPUNOV
FUNCTIONS
145
5.1
ESTIMATES
FOR
THE
CONVERGENCE
OF
TRAJECTORIES
.
148
5.1.1
EXPONENTIAL
STABILITY
.
148
5.1.2
RATIONAL
STABILITY
.
149
5.1.3
FINITE-TIME
STABILITY
.
153
5.2
ANALYTICITY
.
154
5.2.1
ANALYTIC
UNSOLVABILITY
OF
THE
STABILITY
PROBLEM
.
154
5.2.2
ANALYTIC
LIAPUNOV
FUNCTIONS
.
155
5.2.3
HOLOMORPHIC
SYSTEMS
.
158
5.3
WEIGHTED
HOMOGENEITY
.
158
XI
5.3.1
A
FEW
DEFINITIONS
.
159
5.3.2
HOMOGENEOUS
LIAPUNOV
FUNCTIONS
.
161
5.3.3
APPLICATION
TO
THE
STABILIZATION
PROBLEM
.
163
5.4
SYMMETRIES
AND
LIAPUNOV
FUNCTIONS
.
169
5.4.1
DISCRETE
SYMMETRY
.
170
5.4.2
INFINITESIMAL
SYMMETRY
.
171
5.4.3
SYMMETRIC
LIAPUNOV
FUNCTIONS
.
174
6
MONOTONICITY
AND
GENERALIZED
DERIVATIVES
181
6.1
TOOLS
FROM
NONSMOOTH
ANALYSIS
.
181
6.2
FUNCTIONS
OF
ONE
VARIABLE
.
185
6.3
ORDINARY
DIFFERENTIAL
EQUATIONS
.
187
6.4
DIFFERENTIAL
INCLUSIONS
.
190
6.5
MONOTONICITY
AND
THE
PROXIMAL
GRADIENT
.
193
BIBLIOGRAPHY
195 |
| any_adam_object | 1 |
| author | Bacciotti, Andrea 1948- Rosier, Lionel 1967- |
| author_GND | (DE-588)122673921 (DE-588)12267393X |
| author_facet | Bacciotti, Andrea 1948- Rosier, Lionel 1967- |
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| author_sort | Bacciotti, Andrea 1948- |
| author_variant | a b ab l r lr |
| building | Verbundindex |
| bvnumber | BV013605023 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA402.3 |
| callnumber-search | QA402.3 |
| callnumber-sort | QA 3402.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 845 |
| ctrlnum | (OCoLC)45908899 (DE-599)BVBBV013605023 |
| 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 |
| format | Book |
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| id | DE-604.BV013605023 |
| illustrated | Illustrated |
| indexdate | 2024-08-13T00:15:13Z |
| institution | BVB |
| isbn | 1852334193 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009293992 |
| oclc_num | 45908899 |
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| owner | DE-739 DE-703 DE-706 DE-634 DE-83 |
| owner_facet | DE-739 DE-703 DE-706 DE-634 DE-83 |
| physical | XI, 208 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Bacciotti, Andrea 1948- Verfasser (DE-588)122673921 aut Liapunov functions and stability in control theory Andrea Bacciotti and Lionel Rosier London ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong Springer 2001 XI, 208 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 267 Commande, Théorie de la ram Liapounov, Fonctions de ram Stabilité ram Control theory Lyapunov functions Stability Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 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 Lecture notes in control and information sciences 267 (DE-604)BV005848579 267 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009293992&sequence=000001&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 Lecture notes in control and information sciences Commande, Théorie de la ram Liapounov, Fonctions de ram Stabilité ram Control theory Lyapunov functions Stability Kontrolltheorie (DE-588)4032317-1 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4167992-1 |
| 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 | Commande, Théorie de la ram Liapounov, Fonctions de ram Stabilité ram Control theory Lyapunov functions Stability Kontrolltheorie (DE-588)4032317-1 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| topic_facet | Commande, Théorie de la Liapounov, Fonctions de Stabilité Control theory Lyapunov functions Stability Kontrolltheorie Ljapunov-Stabilitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009293992&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005848579 |
| work_keys_str_mv | AT bacciottiandrea liapunovfunctionsandstabilityincontroltheory AT rosierlionel liapunovfunctionsandstabilityincontroltheory |