Qualitative methods in nonlinear dynamics: novel approaches to Liapunov's matrix functions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
2002
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| Schriftenreihe: | Pure and applied mathematics
246 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 301 S. graph. Darst. |
| ISBN: | 0824707354 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | QUALITATIVE METHODS IN NONLINEAR DYNAMICS NOVEL APPROACHES TO LIAPUNOV S
MATRIX FUNCTIONS A. A. MARTYNYUK INSTITUTE OF MECHANICS NATIONAL ACADEMY
OF SCIENCES OF UKRAINE KIEV, UKRAINE MARCEL DEKKER, INC. NEW YORK *
BASEL CONTENTS PREFACE III 1 PRELIMINARIES 1 1.1 INTRODUCTION 1 1.2
NONLINEAR CONTINUOUS SYSTEMS 2 1.2.1 GENERAL EQUATIONS OF NONLINEAR
DYNAMICS 2 1.2.2 PERTURBED MOTION EQUATIONS 3 1.3 DEFINITIONS OF
STABILITY 5 1.4 SCALAR, VECTOR AND MATRIX-VALUED LIAPUNOV FUNCTIONS 8
1.4.1 AUXILIARY SCALAR FUNCTIONS 8 1.4.2 COMPARISON FUNCTIONS 9 1.4.3
VECTOR LIAPUNOV FUNCTIONS 14 1.4.4 MATRIX-VALUED METAFUNCTION 15 1.5
COMPARISON PRINCIPLE 17 1.6 LIAPUNOV-LIKE THEOREMS 23 1.6.1
MATRIX-VALUED FUNCTION AND ITS PROPERTIES 23 1.6.2 A VERSION OF THE
ORIGINAL THEOREMS OF LIAPUNOV 26 1.7 ADVANTAGES OF CONE-VALUED LIAPUNOV
FUNCTIONS 33 1.7.1 STABILITY WITH RESPECT TO TWO MEASURES 34 1.7.2
STABILITY ANALYSIS OF LARGE SCALE SYSTEMS 36 1.8 LIAPUNOV S THEOREMS FOR
LARGE SCALE SYSTEMS IN GENERAL 41 1.8.1 WHY ARE MATRIX-VALUED LIAPUNOV
FUNCTIONS NEEDED? 41 1.8.2 STABILITY AND INSTABILITY OF LARGE SCALE
SYSTEMS 42 1.9 NOTES 47 2 QUALITATIVE ANALYSIS OF CONTINUOUS SYSTEMS 49
2.1 INTRODUCTION 49 VII II CONTENTS 2.2 NONLINEAR SYSTEMS WITH MIXED
HIERARCHY OF SUBSYSTEMS 50 2.2.1 MIXED HIERARCHICAL STRUCTURES 50 2.2.2
HIERARCHICAL MATRIX FUNCTION STRUCTURE 52 2.2.3 STRUCTURE OF
HIERARCHICAL MATRIX FUNCTION DERIVATIVE 56 2.2.4 STABILITY AND
INSTABILITY CONDITIONS 59 2.2.5 LINEAR AUTONOMOUS SYSTEM, 60 2.2.6
EXAMPLES OF THIRD ORDER SYSTEMS 63 2.3 DYNAMICS OF THE SYSTEMS WITH
REGULAR HIERARCHY SUBSYSTEMS 68 2.3.1 IKEDA-SILJAK HIERARCHICAL
DECOMPOSITION 68 2.3.2 HIERARCHICAL LIAPUNOV S MATRIX-VALUED FUNCTIONS
69 2.3.3 STABILITY AND INSTABILITY CONDITIONS 74 2.3.4 LINEAR
NONAUTONOMOUS SYSTEMS 79 2.4 STABILITY ANALYSIS OF LARGE SCALE SYSTEMS
90 2.4.1 A CLASS OF LARGE SCALE SYSTEMS 90 2.4.2 CONSTRUCTION OF
NONDIAGONAL ELEMENTS OF MATRIX-VALUED FUNCTION 91 2.4.3 TEST FOR
STABILITY ANALYSIS 94 2.4.4 LINEAR LARGE SCALE SYSTEM 94 2.4.5
DISCUSSION AND NUMERICAL EXAMPLE 97 2.5 OVERLAPPING DECOMPOSITION AND
MATRIX-VALUED FUNCTION CONSTRUCTION 100 2.5.1 DYNAMICAL SYSTEM EXTENSION
100 2.5.2 LIAPUNOV MATRIX-VALUED FUNCTION CONSTRUCTION 105 2.5.3 TEST
FOR STABILITY OF SYSTEM (2.5.1) 105 2.5.4 NUMERICAL EXAMPLE 106 2.6
EXPONENTIAL POLYSTABILITY ANALYSIS OF SEPARABLE MOTIONS 108 2.6.1
STATEMENT OF THE PROBLEM 108 2.6.2 A METHOD FOR THE SOLUTION OF THE
PROBLEM 110 2.6.3 AUTONOMOUS SYSTEM 118 2.6.4 POLYSTABILITY BY THE FIRST
ORDER APPROXIMATIONS 122 2.7 INTEGRAL AND LIPSCHITZ STABILITY 127 2.7.1
DEFINITIONS 127 2.7.2 SUFFICIENT CONDITIONS FOR INTEGRAL AND ASYMPTOTIC
INTEGRAL STABILITY 128 2.7.3 UNIFORM LIPSCHITZ STABILITY 133 2.8 NOTES
135 CONTENTS IX 3 QUALITATIVE ANALYSIS OF DISCRETE-TIME SYSTEMS 139 3.1
INTRODUCTION 139 3.2 SYSTEMS DESCRIBED BY DIFFERENCE EQUATIONS 140 3.3
MATRIX-VALUED LIAPUNOV FUNCTIONS METHOD 143 3.3.1 AUXILIARY RESULTS 143
3.3.2 COMPARISON PRINCIPLE APPLICATION 144 3.3.3 GENERAL THEOREMS ON
STABILITY 147 3.4 LARGE SCALE SYSTEM DECOMPOSITION 149 3.5 STABILITY AND
INSTABILITY OF LARGE SCALE SYSTEMS 151 3.5.1 AUXILIARY ESTIMATES 151
3.5.2 STABILITY AND INSTABILITY CONDITIONS 157 3.6 AUTONOMOUS LARGE
SCALE SYSTEMS 159 3.7 HIERARCHICAL ANALYSIS OF STABILITY 166 3.7.1
HIERARCHICAL DECOMPOSITION AND STABILITY CONDITIONS 166 3.7.2 NOVEL
TESTS FOR CONNECTIVE STABILITY 172 3.8 CONTROLLED SYSTEMS 179 3.9 NOTES
181 4 NONLINEAR DYNAMICS OF IMPULSIVE SYSTEMS 183 4.1 INTRODUCTION 183
4.2 LARGE SCALE IMPULSIVE SYSTEMS IN GENERAL 184 4.2.1 NOTATIONS AND
DEFINITIONS 184 4.2.2 AUXILIARY RESULTS 186 4.2.3 SUFFICIENT STABILITY
CONDITIONS 195 4.2.4 INSTABILITY CONDITIONS 197 4.3 HIERARCHICAL
IMPULSIVE SYSTEMS 201 4.4 ANALYTICAL CONSTRUCTION OF LIAPUNOV FUNCTION
204 4.4.1 STRUCTURE OF HIERARCHICAL MATRIX-VALUED LIAPUNOV FUNCTION 204
4.4.2 STRUCTURE OF THE TOTAL DERIVATIVE OF HIERARCHICAL MATRIX-VALUED
FUNCTION 207 4.5 UNIQUENESS AND CONTINUABILITY OF SOLUTIONS 215 4.6 ON
BOUNDEDNESS OF THE SOLUTIONS 222 4.7 NOVEL METHODOLOGY FOR STABILITY 228
4.7.1 STABILITY CONDITIONS 228 4.8 NOTES 238 X CONTENTS 5 APPLICATIONS
239 5.1 INTRODUCTION 239 5.2 ESTIMATIONS OF ASYMPTOTIC STABILITY DOMAINS
IN GENERAL 239 5.2.1 A FUNDAMENTAL ZUBOV S RESULT 239 5.2.2 SOME
ESTIMATES FOR QUADRATIC MATRIX-VALUED FUNCTIONS 241 5.2.3 ALGORITHM OF
CONSTRUCTING A POINT NETWORK COVERING BOUNDARY OF DOMAIN E 245 5.2.4
NUMERICAL REALIZATION AND DISCUSSION OF THE ALGORITHM 250 5.2.5
ILLUSTRATIVE EXAMPLES 254 5.3 CONSTRUCTION OF ESTIMATE FOR THE DOMAIN E
OF POWER SYSTEM 263 5.4 OSCILLATIONS AND STABILITY OF SOME MECHANICAL
SYSTEMS 267 5.4.1 THREE-MASS SYSTEMS 267 5.4.2 NONAUTONOMOUS OSCILLATOR
269 5.5 ABSOLUTE STABILITY OF DISCRETE SYSTEMS 270 5.6 NOTES 274
REFERENCES 277 SUBJECT INDEX 295
|
| any_adam_object | 1 |
| author | Martynjuk, Anatolij A. 1941- |
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| bvnumber | BV014106427 |
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| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:57:45Z |
| institution | BVB |
| isbn | 0824707354 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009663959 |
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| series2 | Pure and applied mathematics |
| spelling | Martynjuk, Anatolij A. 1941- Verfasser (DE-588)1020347279 aut Qualitative methods in nonlinear dynamics novel approaches to Liapunov's matrix functions A. A. Martynyuk New York [u.a.] Dekker 2002 X, 301 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 246 Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Matrixwertige Funktion (DE-588)4128928-6 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s Stabilität (DE-588)4056693-6 s Matrixwertige Funktion (DE-588)4128928-6 s DE-604 Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s Pure and applied mathematics 246 (DE-604)BV000001885 246 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009663959&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martynjuk, Anatolij A. 1941- Qualitative methods in nonlinear dynamics novel approaches to Liapunov's matrix functions Pure and applied mathematics Nichtlineare Dynamik (DE-588)4126141-0 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Stabilität (DE-588)4056693-6 gnd Matrixwertige Funktion (DE-588)4128928-6 gnd |
| subject_GND | (DE-588)4126141-0 (DE-588)4167992-1 (DE-588)4056693-6 (DE-588)4128928-6 |
| title | Qualitative methods in nonlinear dynamics novel approaches to Liapunov's matrix functions |
| title_auth | Qualitative methods in nonlinear dynamics novel approaches to Liapunov's matrix functions |
| title_exact_search | Qualitative methods in nonlinear dynamics novel approaches to Liapunov's matrix functions |
| title_full | Qualitative methods in nonlinear dynamics novel approaches to Liapunov's matrix functions A. A. Martynyuk |
| title_fullStr | Qualitative methods in nonlinear dynamics novel approaches to Liapunov's matrix functions A. A. Martynyuk |
| title_full_unstemmed | Qualitative methods in nonlinear dynamics novel approaches to Liapunov's matrix functions A. A. Martynyuk |
| title_short | Qualitative methods in nonlinear dynamics |
| title_sort | qualitative methods in nonlinear dynamics novel approaches to liapunov s matrix functions |
| title_sub | novel approaches to Liapunov's matrix functions |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Stabilität (DE-588)4056693-6 gnd Matrixwertige Funktion (DE-588)4128928-6 gnd |
| topic_facet | Nichtlineare Dynamik Ljapunov-Stabilitätstheorie Stabilität Matrixwertige Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009663959&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT martynjukanatolija qualitativemethodsinnonlineardynamicsnovelapproachestoliapunovsmatrixfunctions |