On positive definite solutions to the algebraic Riccati equation
type: Item
instance of: scholarly article
title: On positive definite solutions to the algebraic Riccati equation
zbMATH Open document ID: 0589.15009
DOI: 10.1016/0167-6911(86)90014-9
author: B. George
published in: Systems \& Control Letters
publication date: 1986-01-01T00:00:00Z
review text: The authors study positive definite solutions of the algebraic Riccati equation (ARE) \(\bar AP+PA-PB\bar BP+\bar CC=0,\) where A, B, C are respectively \(n\times n\), \(n\times m\) and \(p\times n\) real matrices and \(\bar X\) denotes the transpose of X. The discussion is only on the real symmetric solution P. The authors first show that if a positive definite solution exists, the system can be decomposed in such a way as to separate out the unstabilizable, undetectable part from the remainder, which is stabilizable. (These properties are those of the optimal control problem for linear time invariant system associated with the ARE.) Finally, necessary and sufficient conditions are provided for the existence of a positive definite solution.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93B25
zbMATH DE Number: 3946358
zbMATH Keywords: Hamiltonian matrix
zbMATH Keywords: stabilizability
zbMATH Keywords: detectability
zbMATH Keywords: positive definite solutions
zbMATH Keywords: algebraic Riccati equation
MaRDI profile type: Publication
full work available at URL: 0167-6911(86)90014-9
OpenAlex ID: W2056075940
cites work: Q3254327
cites work: A contribution to matrix quadratic equations
cites work: Q4765643
cites work: On nonnegative definite solutions to matrix quadratic equations
cites work: On the matrix Riccati equation
cites work: The time-invariant linear-quadratic optimal control problem
cites work: Q4074739
description: scientific article; zbMATH DE number 3946358