On the discrete Riccati equation and its applications to discrete Hamiltonian systems
type: Item
instance of: scholarly article
title: On the discrete Riccati equation and its applications to discrete Hamiltonian systems
zbMATH Open document ID: 0836.39003
author: Pengxiang Yan
author: Lynn Erbe
published in: Rocky Mountain Journal of Mathematics
publication date: 1995-09-17T00:00:00Z
review text: The authors derive comparison theorems for discrete Riccati systems and sufficient conditions of disconjugacy for such autonomous systems, that is, systems with constant coefficient matrices. Applications are made to discrete Hamiltonian vector difference systems introduced by the authors [Proc. Am. Math. Soc., 119, No. 2, 525-533 (1993; Zbl 0794.39006)]. An application is also made to the existence of an optimal control of discrete Hamiltonian systems and the final discussion is summarized in a conjecture on the existence of a Hamiltonian solution to a Riccati equation.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 796913
zbMATH Keywords: comparison theorems
zbMATH Keywords: discrete Riccati systems
zbMATH Keywords: disconjugacy
zbMATH Keywords: autonomous systems
zbMATH Keywords: discrete Hamiltonian vector difference systems
zbMATH Keywords: optimal control
zbMATH Keywords: Hamiltonian solution
zbMATH Keywords: Riccati equation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072275
OpenAlex ID: W1989154070
cites work: Continued Fraction Representations of Maximal and Minimal Solutions of a Discrete Matrix Riccati Equation
cites work: Dominant and recessive solutions of symmetric three term recurrences
cites work: Equivalence of discrete Euler equations and discrete Hamiltonian systems
cites work: Disconjugacy
cites work: Weighted Averaging Techniques in Oscillation Theory for Second Order Difference Equations
cites work: Disconjugacy for linear Hamiltonian difference systems
cites work: Qualitative properties of Hamiltonian difference systems
cites work: Oscillation Criteria for Hamiltonian Matrix Difference Systems
cites work: Higher order Wirtinger inequalities
cites work: Oscillation of second order linear matrix difference equations
cites work: \(C\)-disfocality for linear Hamiltonian difference systems
cites work: Existence and comparison theorems for algebraic Riccati equations for continuous- and discrete-time systems
cites work: Q3360522
DOI: 10.1216/RMJM/1181072275
description: scientific article; zbMATH DE number 796913