Liapunov functions and stability in control theory:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
2005
|
| Edition: | 2. ed. |
| Series: | Communications and control engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 235 S. graph. Darst. |
| ISBN: | 3540213325 9783540213321 |
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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 |
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Record in the Search Index
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|---|---|
| adam_text | ANDREA BACCIOTTI AND LIONEL ROSIER LIAPUNOV FUNCTIONS AND STABILITY IN
CONTROL THEORY 2 ND EDITION WITH 20 FIGURES SPRINGER CONTENTS PREFACE V
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 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 2.2.5 STABILITY AND ROBUSTNESS 44 2.2.6 THE
INVARIANCE PRINCIPLE 47 2.2.7 THE DOMAIN OF ATTRACTION 49 2.2.8
COMPARISON FUNCTIONS 55 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 105
3.4.2 UNIFORM STABILITY 105 3.5 ROBUST STABILITY 108 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 EXPONENTIAL
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 6 MONOTONICITY AND
GENERALIZED DERIVATIVES 203 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 219 INDEX 233 LIST OF ABBREVIATIONS 237
|
| any_adam_object | 1 |
| author | 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 | BV019706533 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.3 |
| callnumber-search | QA402.3 |
| callnumber-sort | QA 3402.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 880 |
| ctrlnum | (OCoLC)61115930 (DE-599)BVBBV019706533 |
| 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. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:04:16Z |
| institution | BVB |
| isbn | 3540213325 9783540213321 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013034001 |
| oclc_num | 61115930 |
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| owner | DE-20 DE-703 DE-824 DE-706 |
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| physical | XIII, 235 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| 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. Berlin [u.a.] Springer 2005 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 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013034001&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 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=013034001&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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