Ordinary differential equations with constant coefficient:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
American Math. Soc.
1997
|
| Series: | Translations of mathematical monographs
169 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | IX, 282 S. graph. Darst. |
| ISBN: | 0821806564 |
Staff View
MARC
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| 100 | 1 | |a Godunov, Sergej K. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Obyknovennye differencial'nye uravnenija s postojannymi koėfficientami |
| 245 | 1 | 0 | |a Ordinary differential equations with constant coefficient |c S. K. Godunov |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1997 | |
| 300 | |a IX, 282 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 169 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 7 | |a Equations différentielles |2 ram | |
| 650 | 7 | |a FONCTION LYAPOUNOV |2 inriac | |
| 650 | 7 | |a MONOGRAPHIE |2 inriac | |
| 650 | 7 | |a SYSTEME CONTROLE LINEAIRE |2 inriac | |
| 650 | 7 | |a stabilité |2 inriac | |
| 650 | 7 | |a système linéaire |2 inriac | |
| 650 | 7 | |a équation Lyapunov |2 inriac | |
| 650 | 7 | |a équation differentielle ordinaire |2 inriac | |
| 650 | 7 | |a équation linéaire |2 inriac | |
| 650 | 4 | |a Differential equations | |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |D s |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Chapter 1. Matrix Exponentials, Green Matrices, and the Lopatinskii Con¬
dition 1
§1. Linear systems of equations with constant coefficients. The unique¬
ness and existence of a solution to the Cauchy problem for homo¬
geneous equations 1
§2. Fundamental matrices and matrix exponentials 9
§3. Estimates for the matrix exponential. Polynomial representation
of the matrix exponential 14
§4. Fundamental systems of solutions to a linear equation of higher
order 21
§5. The continuation of the study of fundamental systems of solutions
to a linear equation of higher order 32
§6. Computation of the matrix exponential by means of reducing ma¬
trices to the Jordan form 43
§7. The definition of a Green matrix. Existence and uniqueness 49
§8. The polynomial representation of the Green matrix. Green func¬
tions 53
§9. Nonhomogeneous linear equations 62
§10. The representation of the matrix exponential and of the Green
matrix by contour integrals 76
§11. Boundary value problem on a segment 82
§12. The closeness estimates for solutions to the boundary value prob¬
lems with close coefficients and close right hand sides 90
§13. The Lopatinskii condition 96
§14. The Green matrices for boundary value problems on a half line 105
Chapter 2. Quadratic Lyapunov Functions 111
§1. Sufficient conditions for the global existence of a solution to a vec¬
tor differential equation 111
§2. The Lyapunov stability 118
§3. The matrix Lyapunov equation 123
§4. The Lyapunov functions 128
§5. The theorems on stability from the first approximation 135
§6. The Hermite theorem 141
§7. The Routh Hurwitz criterion for stability 150
vii
viii CONTENTS
Chapter 3. Qualitative Properties of Problems and Algorithmic Aspects 159
§1. The computation of the matrix exponential and solution of the
Cauchy problem 159
§2. Computational difficulties in the Hurwitz problem and their solu¬
tions 165
§3. Solving of boundary value problems by the orthogonal sweep
method 174
§4. The two way sweep for the computation of the Green matrices 186
§5. Integral and local estimates for the Green matrix 191
§6. Computation of the Green matrix on an infinite line and the de¬
termination of the dichotomy parameter 197
Chapter 4. Linear Control Systems 209
§1. Controllability and observability 209
§2. The simplest variational control problem 214
§3. Stabilizability 231
§4. Variational approach to the construction of a stabilizing control 237
§5. Hamiltonian systems of equations and their use in the study of
stabilizability 242
§6. Further study of variational problems on a half line. The notion of
detectability 250
§7. The Lur e Riccati matrix equation 263
§8. The use of variational problems in the study of control systems 271
References 279
Index 281
|
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| author_facet | Godunov, Sergej K. |
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| author_sort | Godunov, Sergej K. |
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| ctrlnum | (OCoLC)36817338 (DE-599)BVBBV011935279 |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV011935279 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:18:47Z |
| institution | BVB |
| isbn | 0821806564 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008067487 |
| oclc_num | 36817338 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-824 DE-11 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-824 DE-11 |
| physical | IX, 282 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Godunov, Sergej K. Verfasser aut Obyknovennye differencial'nye uravnenija s postojannymi koėfficientami Ordinary differential equations with constant coefficient S. K. Godunov Providence, RI American Math. Soc. 1997 IX, 282 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 169 Aus dem Russ. übers. Equations différentielles ram FONCTION LYAPOUNOV inriac MONOGRAPHIE inriac SYSTEME CONTROLE LINEAIRE inriac stabilité inriac système linéaire inriac équation Lyapunov inriac équation differentielle ordinaire inriac équation linéaire inriac Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Translations of mathematical monographs 169 (DE-604)BV000002394 169 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008067487&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Godunov, Sergej K. Ordinary differential equations with constant coefficient Translations of mathematical monographs Equations différentielles ram FONCTION LYAPOUNOV inriac MONOGRAPHIE inriac SYSTEME CONTROLE LINEAIRE inriac stabilité inriac système linéaire inriac équation Lyapunov inriac équation differentielle ordinaire inriac équation linéaire inriac Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4020929-5 |
| title | Ordinary differential equations with constant coefficient |
| title_alt | Obyknovennye differencial'nye uravnenija s postojannymi koėfficientami |
| title_auth | Ordinary differential equations with constant coefficient |
| title_exact_search | Ordinary differential equations with constant coefficient |
| title_full | Ordinary differential equations with constant coefficient S. K. Godunov |
| title_fullStr | Ordinary differential equations with constant coefficient S. K. Godunov |
| title_full_unstemmed | Ordinary differential equations with constant coefficient S. K. Godunov |
| title_short | Ordinary differential equations with constant coefficient |
| title_sort | ordinary differential equations with constant coefficient |
| topic | Equations différentielles ram FONCTION LYAPOUNOV inriac MONOGRAPHIE inriac SYSTEME CONTROLE LINEAIRE inriac stabilité inriac système linéaire inriac équation Lyapunov inriac équation differentielle ordinaire inriac équation linéaire inriac Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Equations différentielles FONCTION LYAPOUNOV MONOGRAPHIE SYSTEME CONTROLE LINEAIRE stabilité système linéaire équation Lyapunov équation differentielle ordinaire équation linéaire Differential equations Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008067487&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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