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@article{701710,
author = {Hilscher, Roman and Růžičková, Viera},
article_location = {Delhi (Indie)},
article_number = {1},
keywords = {Discrete symplectic system; Quadratic functional; Nonnegativity; Positivity; Riccati inequality; Riccati equation; Conjoined basis; Sturmian theorem},
language = {eng},
issn = {0973-6069},
journal = {International Journal of Difference Equations},
title = {Implicit Riccati equations and quadratic functionals for discrete symplectic systems},
volume = {1},
year = {2006}
}
TY - JOUR
ID - 701710
AU - Hilscher, Roman - Růžičková, Viera
PY - 2006
TI - Implicit Riccati equations and quadratic functionals for discrete symplectic systems
JF - International Journal of Difference Equations
VL - 1
IS - 1
SP - 135-154
EP - 135-154
PB - Research India Publications
SN - 09736069
KW - Discrete symplectic system
KW - Quadratic functional
KW - Nonnegativity
KW - Positivity
KW - Riccati inequality
KW - Riccati equation
KW - Conjoined basis
KW - Sturmian theorem
N2 - 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.
ER -
HILSCHER, Roman a Viera RŮŽIČKOVÁ. Implicit Riccati equations and quadratic functionals for discrete symplectic systems. \textit{International Journal of Difference Equations}. Delhi (Indie): Research India Publications, 2006, roč.~1, č.~1, s.~135-154. ISSN~0973-6069.
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