Stability of motion of nonautonomous systems: (method of limiting equations)
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Luxembourg [u.a.]
Gordon and Breach
1996
|
| Schriftenreihe: | Stability and control
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 255 S. |
| ISBN: | 2884490353 |
Internformat
MARC
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| 100 | 1 | |a Kato, Junji |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stability of motion of nonautonomous systems |b (method of limiting equations) |c J. Kato ; A. A. Martynyuk ; A. A. Shestakov |
| 264 | 1 | |a Luxembourg [u.a.] |b Gordon and Breach |c 1996 | |
| 300 | |a XVIII, 255 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Stability and control |v 3 | |
| 650 | 4 | |a Stability | |
| 650 | 4 | |a System analysis | |
| 650 | 0 | 7 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtautonomes System |0 (DE-588)4480820-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtautonomes System |0 (DE-588)4480820-3 |D s |
| 689 | 0 | 1 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 0 | 2 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Martynjuk, Anatolij A. |d 1941- |e Verfasser |0 (DE-588)1020347279 |4 aut | |
| 700 | 1 | |a Shestakov, A. A. |e Verfasser |4 aut | |
| 830 | 0 | |a Stability and control |v 3 |w (DE-604)BV010641392 |9 3 | |
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Datensatz im Suchindex
| _version_ | 1804127305180643328 |
|---|---|
| adam_text | Contents
Introduction to the Series xi
Foreword xiii
Preface to the English edition xv
Notation xvii
1 Stability Analysis of ODEs by the Method of Limiting Equations
1.0 Introduction 1
1.0.1 Nonautonomous equations 1
1.1 Limiting equations 4
1.2 Some properties of solutions of limiting equations 7
1.3 Uniform asymptotic stability 9
1.4 Eventual properties of solutions 12
1.5 Converse theorems 17
1.5.1 Boundedness 17
1.5.2 Stability and attraction 22
1.6 Stability under perturbations 23
1.6.1 Stability in the sense of Duboshin 24
1.6.2 Stability under PP in almost periodic systems 25
1.7 Lipschitz stability 31
1.8 An application of Lyapunov s direct method in conjunction
with the method of limiting equations 35
vi CONTENTS
1.8.1 Invariant properties and the principle of invariance 35
1.8.2 Localization of compact sets 36
1.8.3 Uniform asymptotic stability 38
1.9 Comments and References 41
2 Limiting Equations and Stability of Infinite Delay Systems
2.0 Introduction 43
2.1 Phase space of a system with infinite delay 43
2.1.1 B space 43
2.1.2 Examples of B spaces 44
2.2 Definitions of stability in B space 44
2.3 Limiting systems 46
2.4 Relationship between stability in R and stability in B space 50
2.5 Stability in R 52
2.6 Stability under perturbations 62
2.6.1 Preliminary results 62
2.6.2 Theorem on stability 63
2.6.3 Stability under perturbations from H(F) 66
2.6.4 Stability under perturbations from H(F) with respect
to a given compact set 69
2.6.5 A false conjecture 73
2.7 Stability under disturbances and asymptotic almost periodicity
of solutions 74
2.8 Eventual stability under perturbations 77
2.8.1 Definitions and assumptions 77
2.8.2 Some theorems on eventual stability 78
2.9 Comments and References 81
3 Limiting Systems and Stability of Motion under Small Forces
3.0 Introduction 83
3.1 Preliminary remarks 83
3.1.1 Description of the system 83
3.1.2 Preliminary results 85
3.2 A stability theorem 87
3.2.1 General theorem 87
CONTENTS vii
3.3 Stability of large scale systems with weakly interacting
subsystems 91
3.3.1 Preliminary notes and definitions 91
3.3.2 Main result 93
3.4 Instability 99
3.5 Instability investigation of large scale systems with weakly
interacting subsystems 103
3.6 Investigation of stability with respect to some variables 106
3.7 Estimation of stability intervals on time variable sets 110
3.7.1 Preliminary results 110
3.7.2 Theorem on estimation of stability intervals Ill
3.7.3 Some corollaries to Theorem 3.7.2 113
3.8 Some applications of the general theorem to mechanical systems 116
3.9 Comments and References 119
4 Stability Analysis of Solutions of ODEs (Continued)
4.0 Introduction 121
4.1 Preliminary results 121
4.2 Theorems on stability and uniform asymptotic stability 124
4.3 An instability theorem 128
4.4 Asymptotic stability and uniform asymptotic stability
with respect to some variables 130
4.5 Instability with respect to some variables 133
4.6 Some models of Lagrangian mechanics 134
4.7 Comments and References 136
5 Stability of Integro Differential Systems
5.0 Introduction 139
5.1 Statement of the problem 139
5.2 Stability theorems 141
5.3 Almost periodic solutions 146
5.4 Population models 151
5.4.1 Investigation of periodic (almost periodic) systems 151
5.4.2 Existence of a strictly positive (componentwise)
almost periodic solution 155
viii CONTENTS
5.5 Stability of motion of a viscoelastic cylinder 158
5.6 Comments and References 160
6 Optimal Stabilization of Controlled Motion and Limiting Equations
6.0 Introduction 161
6.1 Problems of controlled system stabilization 161
6.2 Stabilization theorems 163
6.3 Optimal stabilization in the neutral case 170
6.4 Decentralized control systems 172
6.4.1 Statement of the problem 173
6.4.2 Auxiliary transformations 173
6.4.3 The main result 175
6.5 A model from analytical mechanics 177
6.6 Comments and References 179
7 Stability of Abstract Compact and Uniform Dynamical Processes
7.0 Introduction 181
7.1 The generalized direct Lyapunov method for abstract weak
@ + processes on M 181
7.1.1 Description of system and definitions 181
7.1.2 Localization of the limiting set of a 3H+ process on M 182
7.1.3 Localization of the limiting set for a uniform
2)+ process on M 183
7.2 The continuous L functional for a linear wave equation 184
7.2.1 Generation of an asymptotically autonomous 2#+ process 185
7.2.2 Asymptotic stability 187
7.3 The L functional semicontinuous from below for
a hyperbolic equation 189
7.3.1 Generation of a uniform Q)+ process 190
7.3.2 Convergence of solutions 191
7.3.3 Construction of the L functional 193
7.4 The continuous L functional for an integro differential equation 193
7.4.1 Generation of a weak @ + system 195
7.4.2 Asymptotic stability 196
7.4.3 An application 198
CONTENTS ix
7.5 Comments and References 199
8 Stability in Abstract Dynamical Processes on Convergence Space
8.0 Introduction 201
8.1 Abstract dynamical processes on convergence space, and
reduction of a dynamical process to a dynamical system 201
8.1.1 Semidynamical process on convergence space 202
8.1.2 Reduction of an abstract 3 + process 204
8.2 The generalized Lyapunov direct method for abstract
autonomous Q)+ processes 205
8.3 The generalized Lyapunov direct method for abstract
asymptotically autonomous 2 + processes 208
8.4 The generalized Lyapunov direct method for an abstract
nonautonomous S + process 211
8.4.1 Ball type L functionals and limiting L functional 211
8.4.2 Localization of the limiting set 214
8.5 Application to ODEs of Caratheodory type 216
8.6 Comments and References 220
9 Limiting Lyapunov Functionals for Asymptotically Autonomous
Evolutionary Equations of Parabolic and Hyperbolic Type in
a Banach Space
9.0 Introduction 221
9.1 The generalized Lyapunov direct method for asymptotically
autonomous evolutionary problems of parabolic type 221
9.1.1 Evolutionary problems of parabolic type 221
9.1.2 Localization of the limiting set 223
9.1.3 The limiting L functional for a boundary value problem
of heat conduction 226
9.2 The generalized Lyapunov direct method for asymptotically
autonomous evolutionary equations of hyperbolic type 227
9.2.1 Evolutionary problems of hyperbolic type 227
9.2.2 Localization of the limiting set 229
9.2.3 The limiting L functional for an evolutionary equation
for damped oscillations 231
x CONTENTS
9.3 Applications 234
9.4 Comments and References 237
References 239
Index 253
|
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| author | Kato, Junji Martynjuk, Anatolij A. 1941- Shestakov, A. A. |
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| id | DE-604.BV012648485 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:31:14Z |
| institution | BVB |
| isbn | 2884490353 |
| language | English |
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| physical | XVIII, 255 S. |
| publishDate | 1996 |
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| series | Stability and control |
| series2 | Stability and control |
| spelling | Kato, Junji Verfasser aut Stability of motion of nonautonomous systems (method of limiting equations) J. Kato ; A. A. Martynyuk ; A. A. Shestakov Luxembourg [u.a.] Gordon and Breach 1996 XVIII, 255 S. txt rdacontent n rdamedia nc rdacarrier Stability and control 3 Stability System analysis Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Nichtautonomes System (DE-588)4480820-3 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Nichtautonomes System (DE-588)4480820-3 s Differentialgleichung (DE-588)4012249-9 s Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s DE-604 Martynjuk, Anatolij A. 1941- Verfasser (DE-588)1020347279 aut Shestakov, A. A. Verfasser aut Stability and control 3 (DE-604)BV010641392 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008593126&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kato, Junji Martynjuk, Anatolij A. 1941- Shestakov, A. A. Stability of motion of nonautonomous systems (method of limiting equations) Stability and control Stability System analysis Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Nichtautonomes System (DE-588)4480820-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4167992-1 (DE-588)4480820-3 (DE-588)4012249-9 |
| title | Stability of motion of nonautonomous systems (method of limiting equations) |
| title_auth | Stability of motion of nonautonomous systems (method of limiting equations) |
| title_exact_search | Stability of motion of nonautonomous systems (method of limiting equations) |
| title_full | Stability of motion of nonautonomous systems (method of limiting equations) J. Kato ; A. A. Martynyuk ; A. A. Shestakov |
| title_fullStr | Stability of motion of nonautonomous systems (method of limiting equations) J. Kato ; A. A. Martynyuk ; A. A. Shestakov |
| title_full_unstemmed | Stability of motion of nonautonomous systems (method of limiting equations) J. Kato ; A. A. Martynyuk ; A. A. Shestakov |
| title_short | Stability of motion of nonautonomous systems |
| title_sort | stability of motion of nonautonomous systems method of limiting equations |
| title_sub | (method of limiting equations) |
| topic | Stability System analysis Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd Nichtautonomes System (DE-588)4480820-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Stability System analysis Ljapunov-Stabilitätstheorie Nichtautonomes System Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008593126&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010641392 |
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