Riccati equations for linear Hamiltonian systems without controllability condition

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00107305" target="_blank" >RIV/00216224:14310/19:00107305 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.aimsciences.org/article/doi/10.3934/dcds.2019074" target="_blank" >https://www.aimsciences.org/article/doi/10.3934/dcds.2019074</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3934/dcds.2019074" target="_blank" >10.3934/dcds.2019074</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Riccati equations for linear Hamiltonian systems without controllability condition

Popis výsledku v původním jazyce

In this paper we develop new theory of Riccati matrix differential equations for linear Hamiltonian systems, which do not require any controllability assumption. When the system is nonoscillatory, it is known from our previous work that conjoined bases of the system with eventually the same image form a special structure called a genus. We show that for every such a genus there is an associated Riccati equation. We study the properties of symmetric solutions of these Riccati equations and their connection with conjoined bases of the system. For a given genus, we pay a special attention to distinguished solutions at infinity of the associated Riccati equation and their relationship with the principal solutions at infinity of the system in the considered genus. We show the uniqueness of the distinguished solution at infinity of the Riccati equation corresponding to the minimal genus. This study essentially extends and completes the work of W. T. Reid (1964, 1972), W. A. Coppel (1971), P. Hartman (1964), W. Kratz (1995), and other authors who considered the Riccati equation and its distinguished solution at infinity for invertible conjoined bases, i.e., for the maximal genus in our setting.

Název v anglickém jazyce

Riccati equations for linear Hamiltonian systems without controllability condition

Popis výsledku anglicky

In this paper we develop new theory of Riccati matrix differential equations for linear Hamiltonian systems, which do not require any controllability assumption. When the system is nonoscillatory, it is known from our previous work that conjoined bases of the system with eventually the same image form a special structure called a genus. We show that for every such a genus there is an associated Riccati equation. We study the properties of symmetric solutions of these Riccati equations and their connection with conjoined bases of the system. For a given genus, we pay a special attention to distinguished solutions at infinity of the associated Riccati equation and their relationship with the principal solutions at infinity of the system in the considered genus. We show the uniqueness of the distinguished solution at infinity of the Riccati equation corresponding to the minimal genus. This study essentially extends and completes the work of W. T. Reid (1964, 1972), W. A. Coppel (1971), P. Hartman (1964), W. Kratz (1995), and other authors who considered the Riccati equation and its distinguished solution at infinity for invertible conjoined bases, i.e., for the maximal genus in our setting.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA16-00611S" target="_blank" >GA16-00611S: Hamiltonovské a symplektické systémy: oscilační a spektrální teorie</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Discrete & Continuous Dynamical Systems - A

ISSN

1078-0947

e-ISSN

1553-5231

Svazek periodika

39

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

46

Strana od-do

1685-1730

Kód UT WoS článku

000455398400003

EID výsledku v databázi Scopus

2-s2.0-85061344871