Applications of Liapunov methods in stability:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Academic Publishers
1993
|
| Series: | Mathematics and Its Applications
245 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 237 Seiten |
| ISBN: | 0792321200 |
Staff View
MARC
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| 245 | 1 | 0 | |a Applications of Liapunov methods in stability |c by A. Halanay, Faculty of Mathematics, University of Bucharest, Romania, and V. Rǎsvan, Faculty of Control and Computer Engineering, University of Craiova, Craiova, Romania |
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| 490 | 1 | |a Mathematics and Its Applications |v 245 | |
| 650 | 4 | |a Cinétique chimique | |
| 650 | 4 | |a Dynamique population | |
| 650 | 4 | |a Economie | |
| 650 | 4 | |a Fonction Ljapunov | |
| 650 | 4 | |a Lemme Yakubovich-Kalman-Popov | |
| 650 | 7 | |a Liapounov, fonctions de |2 ram | |
| 650 | 4 | |a Machine synchrone | |
| 650 | 4 | |a Modèle Volterra | |
| 650 | 4 | |a Modèle Walras | |
| 650 | 7 | |a Stabilité |2 ram | |
| 650 | 4 | |a Théorème Leonov | |
| 650 | 4 | |a Wirtschaft | |
| 650 | 4 | |a Lyapunov functions | |
| 650 | 4 | |a Lyapunov stability | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
About the Notations xi
1 Introduction 1
References 12
2 Some General Results in Stability Theory 15
2.1 Basic Concepts 15
2.2 Linear Systems with Constant Coefficients. Stability by
the First Approximation 17
2.3 Liapunov Functions 23
2.4 Application of Liapunov Functions in Some Problems of
Hydraulic Engineering 35
Appendix A 50
Appendix B 51
Appendix C 51
Appendix D 52
Appendix E 53
Appendix F 56
Appendix G 58
References 59
vi
3 Stability Problems in Power Engineering 61
3.1 Stability of Synchronous Generators. Mathematical
Models of Synchronous Machine 61
Liapunov Functions Associated with Synchronous Machines 68
Inherent Stability of Synchronous Machines 71
Stability of the Synchronous Machine with Prime Mover
and Speed Governor 74
The Domain of Admissible Manoeuvres 78
The Reduction Principle and Global behaviour of the
Synchronous Generator with Prime Mover and
Speed Governor 80
3.2 Stabilization of Class of Steam Turbines for Heat
Electricity Generation 85
Configurations and Mathematical Models 86
The Invariant Set of the Models 87
Steady States 89
Systems in Deviations and Inherent Stability 91
Stabilization 93
Appendix 1. The Theorem of G.A. Leonov 101
Appendix 2. A Second Order Equation 106
Appendix 3. Liapunov Equations Ill
Appendix 4. The Yakubovich Kalman Popov Lemma . . .113
Appendix 5. A Result Concerning Exponential Stability . . . .117
References 120
4 Stability Problems in Chemical Engineering 125
4.1 First Model in Chemical Kinetics 125
4.2 Stability of Closed Chemical System Subject to Mass
Action Law 131
The Mathematical Model 131
Equilibrium Points 138
The Liapunov Function and its Properties 143
Stability Results and Qualitative Properties 148
vii
4.3 Processes in Plate Columns 153
4.3.1 The Invariant Set of the Model 160
Steady State Solutions 163
Stability of Steady State 173
Appendix 180
References 187
5 Stability Problems in Non Engineering Fields 191
5.1 Stability of Competitive Equilibrium in Walrasian Eco¬
nomic Model . . 191
The Model 191
Properties of the Model 193
Stability 203
5.2 Volterra Models of Interacting Species 205
Other Properties of Dissipative Communities 212
A Simple Model with Harvesting 216
Appendix 1. Existence of Equilibria in Walrasian Economic
Model 222
Appendix 2 231
References 233
Index 235
|
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| discipline | Informatik Mathematik |
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| id | DE-604.BV006622284 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:49:25Z |
| institution | BVB |
| isbn | 0792321200 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004232455 |
| oclc_num | 27146129 |
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| physical | X, 237 Seiten |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Academic Publishers |
| record_format | marc |
| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spelling | Halanay, Aristide 1924-1997 Verfasser (DE-588)113733003 aut Applications of Liapunov methods in stability by A. Halanay, Faculty of Mathematics, University of Bucharest, Romania, and V. Rǎsvan, Faculty of Control and Computer Engineering, University of Craiova, Craiova, Romania Dordrecht [u.a.] Kluwer Academic Publishers 1993 X, 237 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematics and Its Applications 245 Cinétique chimique Dynamique population Economie Fonction Ljapunov Lemme Yakubovich-Kalman-Popov Liapounov, fonctions de ram Machine synchrone Modèle Volterra Modèle Walras Stabilité ram Théorème Leonov Wirtschaft Lyapunov functions Lyapunov stability Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s DE-604 Rǎsvan, V. Verfasser aut Mathematics and Its Applications 245 (DE-604)BV008163334 245 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004232455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Halanay, Aristide 1924-1997 Rǎsvan, V. Applications of Liapunov methods in stability Mathematics and Its Applications Cinétique chimique Dynamique population Economie Fonction Ljapunov Lemme Yakubovich-Kalman-Popov Liapounov, fonctions de ram Machine synchrone Modèle Volterra Modèle Walras Stabilité ram Théorème Leonov Wirtschaft Lyapunov functions Lyapunov stability Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| subject_GND | (DE-588)4167992-1 |
| title | Applications of Liapunov methods in stability |
| title_auth | Applications of Liapunov methods in stability |
| title_exact_search | Applications of Liapunov methods in stability |
| title_full | Applications of Liapunov methods in stability by A. Halanay, Faculty of Mathematics, University of Bucharest, Romania, and V. Rǎsvan, Faculty of Control and Computer Engineering, University of Craiova, Craiova, Romania |
| title_fullStr | Applications of Liapunov methods in stability by A. Halanay, Faculty of Mathematics, University of Bucharest, Romania, and V. Rǎsvan, Faculty of Control and Computer Engineering, University of Craiova, Craiova, Romania |
| title_full_unstemmed | Applications of Liapunov methods in stability by A. Halanay, Faculty of Mathematics, University of Bucharest, Romania, and V. Rǎsvan, Faculty of Control and Computer Engineering, University of Craiova, Craiova, Romania |
| title_short | Applications of Liapunov methods in stability |
| title_sort | applications of liapunov methods in stability |
| topic | Cinétique chimique Dynamique population Economie Fonction Ljapunov Lemme Yakubovich-Kalman-Popov Liapounov, fonctions de ram Machine synchrone Modèle Volterra Modèle Walras Stabilité ram Théorème Leonov Wirtschaft Lyapunov functions Lyapunov stability Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| topic_facet | Cinétique chimique Dynamique population Economie Fonction Ljapunov Lemme Yakubovich-Kalman-Popov Liapounov, fonctions de Machine synchrone Modèle Volterra Modèle Walras Stabilité Théorème Leonov Wirtschaft Lyapunov functions Lyapunov stability Ljapunov-Stabilitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004232455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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