Non-symmetric matrix Riccati equations
type: Item
instance of: scholarly article
title: Non-symmetric matrix Riccati equations
zbMATH Open document ID: 0821.34011
DOI: 10.4171/ZAA/675
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1995-06-06T00:00:00Z
review text: The paper is concerned with the matrix Riccati differential equation \(W' = B_{21} + B_{22} W - WB_{11} - WB_{12}W\) considered with the corresponding algebraic Riccati equation \((W'=0)\). A fundamental representation formula is obtained, containing information on the phase portrait of the matrix equation. All constant, periodic and almost periodic solutions are described.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 34A99
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 761123
zbMATH Keywords: matrix Riccati differential equation
zbMATH Keywords: representation formula
author: Gerhard Freiling
author: G. Jank
MaRDI profile type: Publication
cites work: Necessary conditions for constant solutions of coupled Riccati equations in Nash games
cites work: Polynomial Factorization via the Riccati Equation
cites work: Q3995590
cites work: Q5619754
cites work: Criterion for the convergence of the solution of the Riccati differential equation
cites work: Meromorphe Differentialgleichungen
cites work: Q3693339
cites work: On the zeros of exponential sums and integrals
cites work: On the matrix Riccati equation
cites work: Geometric properties and invariant manifolds of the Riccati equation
cites work: The Matrix Equation $AZ + B - ZCZ - ZD = 0$
cites work: Matrix Quadratic Solutions
cites work: Riccati differential equations
cites work: On the Variety of Invariant Subspaces of a Finite-Dimensional Linear Operator
cites work: Q3323782
cites work: Geometry of the Algebraic Riccati Equation, Part II
full work available at URL: https://doi.org/10.4171/zaa/675
OpenAlex ID: W1988849267
Recommended article: Q4312519
Recommended article: Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices
Recommended article: Q5289942
Recommended article: Q3086650
Recommended article: Q3793641
Recommended article: On a nonlinear Riccati matrix eigenproblem
Recommended article: Closed-form solution of non-symmetric algebraic Riccati matrix equation
Recommended article: Nonlinear matrix equations of the Riccati type arising in mathematical modelling and simulation
Recommended article: Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for M-matrices
Recommended article: Nonsymmetric Algebraic Riccati Equations under the Tensor Product
description: scientific article; zbMATH DE number 761123