Asymptotic properties of solutions of Riccati matrix equations
and inequalities for discrete symplectic systems

J 2015

Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems

ŠIMON HILSCHER, Roman

Basic information

Original name

Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems

Name in Czech

Asymptotické vlastnosti řešení Riccatiho maticových rovnic a nerovnic pro diskrétní symplektické systémy

Authors

ŠIMON HILSCHER, Roman (203 Czech Republic, guarantor, belonging to the institution)

Edition

Electronic Journal of Qualitative Theory of Differential Equations, Szeged, Electronic Journal of Qualitative Theory of Differential Equations, Bolyai Institute, University of Szeged, 2015, 1417-3875

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Hungary

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 0.732

RIV identification code

RIV/00216224:14310/15:00083551

Organization unit

Faculty of Science

UT WoS

000365261100001

Keywords (in Czech)

symplektický systém; Riccatiho maticová rovnice; Riccatiho maticová nerovnice; recesivní řešení; minimální řešení; neoscilace

Keywords in English

Symplectic system; Riccati matrix equation; Riccati matrix inequality; Recessive solution; Distinguished solution; Nonoscillation

Abstract

ORIG CZ

V originále

In this paper we study the asymptotic properties of the distinguished solutions of Riccati matrix equations and inequalities for discrete symplectic systems. In particular, we generalize the inequalities known for symmetric solutions of Riccati matrix equations to Riccati matrix inequalities. We also justify the definition and properties of the distinguished solution and the recessive solution at minus infinity by relating them to their counterparts at plus infinity.

In Czech

V tomto článku studujeme asymptotické vlastnosti minimálních řešení Riccatiho maticových rovnic a nerovnic pro diskrétní symplektické systémy. Zejména zobecňujeme nerovnosti, které jsou známé pro symetrická řešení Riccatiho maticových rovnic, na Riccatiho maticové nerovnice. Taktéž zdůvodňujeme definici a vlastnosti minimálního řešení Riccatiho rovnice a recesivního řešení symplektického systému v mínus nekonečnu pomocí příslušných známých pojmů v plus nekonečnu.

Citovat

ŠIMON HILSCHER, Roman. Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems. Electronic Journal of Qualitative Theory of Differential Equations. Szeged: Electronic Journal of Qualitative Theory of Differential Equations, Bolyai Institute, University of Szeged, 2015, vol. 54, No 54, p. "nestrankovano", 16 pp. ISSN 1417-3875.

@article{1308375,
   author = {Šimon Hilscher, Roman},
   article_location = {Szeged},
   article_number = {54},
   keywords = {Symplectic system; Riccati matrix equation; Riccati matrix inequality; Recessive solution; Distinguished solution; Nonoscillation},
   language = {eng},
   issn = {1417-3875},
   journal = {Electronic Journal of Qualitative Theory of Differential Equations},
   title = {Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems},
   volume = {54},
   year = {2015}
}

TY  - JOUR
ID  - 1308375
AU  - Šimon Hilscher, Roman
PY  - 2015
TI  - Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems
JF  - Electronic Journal of Qualitative Theory of Differential Equations
VL  - 54
IS  - 54
SP  - "nestrankovano"
EP  - "nestrankovano"
PB  - Electronic Journal of Qualitative Theory of Differential Equations, Bolyai Institute, University of Szeged
SN  - 14173875
KW  - Symplectic system
KW  - Riccati matrix equation
KW  - Riccati matrix inequality
KW  - Recessive solution
KW  - Distinguished solution
KW  - Nonoscillation
N2  - In this paper we study the asymptotic properties of the distinguished solutions of Riccati matrix equations and inequalities for discrete symplectic systems. In particular, we generalize the inequalities known for symmetric solutions of Riccati matrix equations to Riccati matrix inequalities. We also justify the definition and properties of the distinguished solution and the recessive solution at minus infinity by relating them to their counterparts at plus infinity.
ER  -

ŠIMON HILSCHER, Roman. Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems. \textit{Electronic Journal of Qualitative Theory of Differential Equations}. Szeged: Electronic Journal of Qualitative Theory of Differential Equations, Bolyai Institute, University of Szeged, 2015, vol.~54, No~54, p.~''nestrankovano'', 16 pp. ISSN~1417-3875.

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