Nonautonomous linear Hamiltonian systems: oscillation, spectral theory and control
This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties o...
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Switzerland
Springer
[2016]
|
| Schriftenreihe: | Developments in mathematics
|
| Schlagworte: | |
| Zusammenfassung: | This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense. The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory |
| Beschreibung: | xxi, 497 Seiten |
| ISBN: | 9783319290232 |
Internformat
MARC
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| 100 | 1 | |a Johnson, Russell |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonautonomous linear Hamiltonian systems |b oscillation, spectral theory and control |c Russell Johnson, Rafael Obaya, Sylvia Novo, Carmen Núñez, Roberta Fabbri |
| 264 | 1 | |a Switzerland |b Springer |c [2016] | |
| 300 | |a xxi, 497 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Developments in mathematics | |
| 505 | 8 | |a Includes bibliographical references and index | |
| 520 | |a This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense. The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory | ||
| 650 | 4 | |a Hamiltonian systems | |
| 650 | 7 | |a MATHEMATICS / Topology |2 bisacsh | |
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hamiltonsches System |0 (DE-588)4139943-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hamiltonsches System |0 (DE-588)4139943-2 |D s |
| 689 | 0 | 1 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | 2 | |a Spektraltheorie |0 (DE-588)4116561-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Obaya, Rafael |e Verfasser |4 aut | |
| 700 | 1 | |a Novo, Sylvia |e Verfasser |4 aut | |
| 700 | 1 | |a Núñez, Carmen |e Verfasser |4 aut | |
| 700 | 1 | |a Fabbri, Roberta |e Verfasser |0 (DE-588)1056240245 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-319-29025-6 |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028915119 | ||
Datensatz im Suchindex
| _version_ | 1804176132543610880 |
|---|---|
| any_adam_object | |
| author | Johnson, Russell Obaya, Rafael Novo, Sylvia Núñez, Carmen Fabbri, Roberta |
| author_GND | (DE-588)1056240245 |
| author_facet | Johnson, Russell Obaya, Rafael Novo, Sylvia Núñez, Carmen Fabbri, Roberta |
| author_role | aut aut aut aut aut |
| author_sort | Johnson, Russell |
| author_variant | r j rj r o ro s n sn c n cn r f rf |
| building | Verbundindex |
| bvnumber | BV043498670 |
| classification_rvk | SK 810 |
| contents | Includes bibliographical references and index |
| ctrlnum | (OCoLC)969455072 (DE-599)BVBBV043498670 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV043498670 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:27:19Z |
| institution | BVB |
| isbn | 9783319290232 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028915119 |
| oclc_num | 969455072 |
| open_access_boolean | |
| owner | DE-384 |
| owner_facet | DE-384 |
| physical | xxi, 497 Seiten |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Springer |
| record_format | marc |
| series2 | Developments in mathematics |
| spelling | Johnson, Russell Verfasser aut Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control Russell Johnson, Rafael Obaya, Sylvia Novo, Carmen Núñez, Roberta Fabbri Switzerland Springer [2016] xxi, 497 Seiten txt rdacontent n rdamedia nc rdacarrier Developments in mathematics Includes bibliographical references and index This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense. The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory Hamiltonian systems MATHEMATICS / Topology bisacsh Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Dynamisches System (DE-588)4013396-5 s Spektraltheorie (DE-588)4116561-5 s DE-604 Obaya, Rafael Verfasser aut Novo, Sylvia Verfasser aut Núñez, Carmen Verfasser aut Fabbri, Roberta Verfasser (DE-588)1056240245 aut Erscheint auch als Online-Ausgabe 978-3-319-29025-6 |
| spellingShingle | Johnson, Russell Obaya, Rafael Novo, Sylvia Núñez, Carmen Fabbri, Roberta Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control Includes bibliographical references and index Hamiltonian systems MATHEMATICS / Topology bisacsh Spektraltheorie (DE-588)4116561-5 gnd Hamiltonsches System (DE-588)4139943-2 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4139943-2 (DE-588)4013396-5 |
| title | Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control |
| title_auth | Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control |
| title_exact_search | Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control |
| title_full | Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control Russell Johnson, Rafael Obaya, Sylvia Novo, Carmen Núñez, Roberta Fabbri |
| title_fullStr | Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control Russell Johnson, Rafael Obaya, Sylvia Novo, Carmen Núñez, Roberta Fabbri |
| title_full_unstemmed | Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control Russell Johnson, Rafael Obaya, Sylvia Novo, Carmen Núñez, Roberta Fabbri |
| title_short | Nonautonomous linear Hamiltonian systems |
| title_sort | nonautonomous linear hamiltonian systems oscillation spectral theory and control |
| title_sub | oscillation, spectral theory and control |
| topic | Hamiltonian systems MATHEMATICS / Topology bisacsh Spektraltheorie (DE-588)4116561-5 gnd Hamiltonsches System (DE-588)4139943-2 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Hamiltonian systems MATHEMATICS / Topology Spektraltheorie Hamiltonsches System Dynamisches System |
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