Publication detail
Implicit Riccati equations and quadratic functionals for discrete symplectic systems
HILSCHER, R. RŮŽIČKOVÁ, V.
Czech title
Implicitní Riccatiho rovnice a kvadratické funkcionály pro diskrétní symplektické systémy
English title
Implicit Riccati equations and quadratic functionals for discrete symplectic systems
Type
journal article - other
Language
en
Original abstract
In this paper we study discrete (implicit) Riccati matrix equations associated with discrete symplectic systems and related quadratic functionals F with variable endpoints. We derive these Riccati equations for nonnegative functionals F with separable and jointly varying endpoints. The result for jointly varying endpoints is in terms of the nonaugmented Riccati operator. The method also allows to simplify implicit Riccati equations known for the positivity of F. Finally, we establish a comparison result (Riccati inequality) for solutions of Riccati equations associated with two discrete symplectic systems.
Czech abstract
V tomto článku studujeme diskrétní (implicitní) Riccatiho maticové rovnice související s diskrétními symplektickými systémy a kvadratickými funkcionály s proměnnými konci. Odvodíme tyto Riccatiho rovnice pro nezáporné funkcionály s oddělenými a obecnými konci. Výsledek pro obecné konce je ve tvaru nerozšířeného Riccatiho operátoru. Metoda dále umožňuje zjednodušit známé implicitní Riccatiho rovnice pro pozitivitu funkcionálu. V závěru uvedeme srovnávací větu pro řešení Riccatiho rovnic náležících různým diskrétním symplektickým systémům.
English abstract
In this paper we study discrete (implicit) Riccati matrix equations associated with discrete symplectic systems and related quadratic functionals F with variable endpoints. We derive these Riccati equations for nonnegative functionals F with separable and jointly varying endpoints. The result for jointly varying endpoints is in terms of the nonaugmented Riccati operator. The method also allows to simplify implicit Riccati equations known for the positivity of F. Finally, we establish a comparison result (Riccati inequality) for solutions of Riccati equations associated with two discrete symplectic systems.
Keywords in English
Discrete symplectic system, Quadratic functional, Nonnegativity, Positivity, Riccati inequality, Riccati equation, Conjoined basis, Sturmian theorem
Released
15.11.2006
Publisher
Research India Publications
ISSN
0973-6069
Journal
International Journal of Difference Equations
Volume
1
Number
1
Pages from–to
135–154
Pages count
20
BIBTEX
@article{BUT43694,
author="Roman Šimon {Hilscher} and Viera {Štoudková Růžičková},
title="Implicit Riccati equations and quadratic functionals for discrete symplectic systems",
journal="International Journal of Difference Equations",
year="2006",
volume="1",
number="1",
month="November",
pages="135--154",
publisher="Research India Publications",
issn="0973-6069"
}