Genera of Conjoined Bases for (Non)oscillatory Linear Hamiltonian Systems: Extended Theory

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114315" target="_blank" >RIV/00216224:14310/20:00114315 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10884-019-09810-w" target="_blank" >https://doi.org/10.1007/s10884-019-09810-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10884-019-09810-w" target="_blank" >10.1007/s10884-019-09810-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Genera of Conjoined Bases for (Non)oscillatory Linear Hamiltonian Systems: Extended Theory

Popis výsledku v původním jazyce

In this paper we study the properties of conjoined bases of a general linear Hamiltonian system without any controllability condition. When the Legendre condition holds and the system is nonoscillatory, it is known from our previous work that conjoined bases with eventually the same image form a special structure called a genus. In this work we extend the theory of genera of conjoined bases to arbitrary systems, for which the Legendre condition is not assumed and/or the system may be oscillatory. We derive a classification of all genera of conjoined bases and show that they form a complete lattice. These results are based on the relationship between subspaces of solutions of a linear control system and orthogonal projectors satisfying a certain Riccati type differential equation. The presented theory is applied in our paper (Sepitka in Discrete Contin Dyn Syst 39(4):1685-1730,2019) to general Riccati matrix differential equations for possibly uncontrollable linear Hamiltonian systems.

Název v anglickém jazyce

Genera of Conjoined Bases for (Non)oscillatory Linear Hamiltonian Systems: Extended Theory

Popis výsledku anglicky

In this paper we study the properties of conjoined bases of a general linear Hamiltonian system without any controllability condition. When the Legendre condition holds and the system is nonoscillatory, it is known from our previous work that conjoined bases with eventually the same image form a special structure called a genus. In this work we extend the theory of genera of conjoined bases to arbitrary systems, for which the Legendre condition is not assumed and/or the system may be oscillatory. We derive a classification of all genera of conjoined bases and show that they form a complete lattice. These results are based on the relationship between subspaces of solutions of a linear control system and orthogonal projectors satisfying a certain Riccati type differential equation. The presented theory is applied in our paper (Sepitka in Discrete Contin Dyn Syst 39(4):1685-1730,2019) to general Riccati matrix differential equations for possibly uncontrollable linear Hamiltonian systems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of dynamics and differential equations.

ISSN

1040-7294

e-ISSN

—

Svazek periodika

32

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

1139-1155

Kód UT WoS článku

000541929200001

EID výsledku v databázi Scopus

2-s2.0-85075386742