Matrix Diagonal Stability in Systems and Computation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2000
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type" Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the special virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors' synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "culture" that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonaltype Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions. This monograph shows that, although this obvious interpretation is often adequate, there are many instances in which the Liapunov approach is best taken advantage of using diagonal-type Liapunov functions. In fact, they yield necessary and sufficient stability conditions for some classes of nonlinear dynamical systems |
| Beschreibung: | 1 Online-Ressource (XIV, 267 p) |
| ISBN: | 9781461213468 9781461271055 |
| DOI: | 10.1007/978-1-4612-1346-8 |
Internformat
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| 500 | |a This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type" Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the special virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors' synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "culture" that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonaltype Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions. This monograph shows that, although this obvious interpretation is often adequate, there are many instances in which the Liapunov approach is best taken advantage of using diagonal-type Liapunov functions. In fact, they yield necessary and sufficient stability conditions for some classes of nonlinear dynamical systems | ||
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Datensatz im Suchindex
| _version_ | 1804153090904948736 |
|---|---|
| any_adam_object | |
| author | Kaszkurewicz, Eugenius |
| author_GND | (DE-588)1146241291 |
| author_facet | Kaszkurewicz, Eugenius |
| author_role | aut |
| author_sort | Kaszkurewicz, Eugenius |
| author_variant | e k ek |
| building | Verbundindex |
| bvnumber | BV042419809 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879621280 (DE-599)BVBBV042419809 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1346-8 |
| format | Electronic eBook |
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| id | DE-604.BV042419809 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461213468 9781461271055 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855226 |
| oclc_num | 879621280 |
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| spelling | Kaszkurewicz, Eugenius Verfasser (DE-588)1146241291 aut Matrix Diagonal Stability in Systems and Computation by Eugenius Kaszkurewicz, Amit Bhaya Boston, MA Birkhäuser Boston 2000 1 Online-Ressource (XIV, 267 p) txt rdacontent c rdamedia cr rdacarrier This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type" Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the special virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors' synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "culture" that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonaltype Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions. This monograph shows that, although this obvious interpretation is often adequate, there are many instances in which the Liapunov approach is best taken advantage of using diagonal-type Liapunov functions. In fact, they yield necessary and sufficient stability conditions for some classes of nonlinear dynamical systems Mathematics Matrix theory Computer science / Mathematics Numerical analysis Linear and Multilinear Algebras, Matrix Theory Numerical Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Matrizenanalysis (DE-588)4227735-8 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Matrix Mathematik (DE-588)4037968-1 s Stabilität (DE-588)4056693-6 s 1\p DE-604 Matrizenanalysis (DE-588)4227735-8 s 2\p DE-604 Bhaya, Amit Sonstige oth https://doi.org/10.1007/978-1-4612-1346-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kaszkurewicz, Eugenius Matrix Diagonal Stability in Systems and Computation Mathematics Matrix theory Computer science / Mathematics Numerical analysis Linear and Multilinear Algebras, Matrix Theory Numerical Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Matrizenanalysis (DE-588)4227735-8 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Stabilität (DE-588)4056693-6 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4227735-8 (DE-588)4137931-7 (DE-588)4056693-6 (DE-588)4037968-1 |
| title | Matrix Diagonal Stability in Systems and Computation |
| title_auth | Matrix Diagonal Stability in Systems and Computation |
| title_exact_search | Matrix Diagonal Stability in Systems and Computation |
| title_full | Matrix Diagonal Stability in Systems and Computation by Eugenius Kaszkurewicz, Amit Bhaya |
| title_fullStr | Matrix Diagonal Stability in Systems and Computation by Eugenius Kaszkurewicz, Amit Bhaya |
| title_full_unstemmed | Matrix Diagonal Stability in Systems and Computation by Eugenius Kaszkurewicz, Amit Bhaya |
| title_short | Matrix Diagonal Stability in Systems and Computation |
| title_sort | matrix diagonal stability in systems and computation |
| topic | Mathematics Matrix theory Computer science / Mathematics Numerical analysis Linear and Multilinear Algebras, Matrix Theory Numerical Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Matrizenanalysis (DE-588)4227735-8 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Stabilität (DE-588)4056693-6 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Mathematics Matrix theory Computer science / Mathematics Numerical analysis Linear and Multilinear Algebras, Matrix Theory Numerical Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Matrizenanalysis Differenzierbares dynamisches System Stabilität Matrix Mathematik |
| url | https://doi.org/10.1007/978-1-4612-1346-8 |
| work_keys_str_mv | AT kaszkurewiczeugenius matrixdiagonalstabilityinsystemsandcomputation AT bhayaamit matrixdiagonalstabilityinsystemsandcomputation |