The zero divisor problem of multivariable stochastic adaptive control
type: Item
instance of: scholarly article
title: The zero divisor problem of multivariable stochastic adaptive control
zbMATH Open document ID: 0579.93067
DOI: 10.1016/0167-6911(85)90073-8
published in: Systems \& Control Letters
publication date: 1985-01-01T00:00:00Z
review text: The main result of the paper is the following theorem: ''Let \(Q(x_ 1,...,x_ n)\) be a real-valued rational function of n real variables which is not constant. Let \(\{w_ 1,...,w_ n\}\) be n random variables which are jointly absolutely continuous (distributed) with respect to Lebesgue measure. Then \(Q(w_ 1,...,w_ n)\) is also absolutely continuous (distributed) with respect to Lebesgue measure.'' This result is obtained proving that \(\mu_ n(Q^{-1}(E))=0\) for every set \(E\subset R\) such that \(\mu_ 1(E)=0\), where \(\mu_ k\) represents the Lebesgue measure on \(R^ k\). This theorem is applied in the analysis of stochastic adaptive minimum variance control algorithms (the zero divisor problem) for linear discrete-time systems.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93E25
zbMATH DE Number: 3928861
zbMATH Keywords: stochastic adaptive minimum variance control algorithms
zbMATH Keywords: linear discrete- time systems
author: Sean P. Meyn
author: Peter E. Caines
MaRDI profile type: Publication
full work available at URL: 0167-6911(85)90073-8
OpenAlex ID: W2021813906
cites work: Discrete Time Stochastic Adaptive Control
cites work: Stochastic adaptive control using a modified least squares algorithm
cites work: On the adaptive control of a class of systems with random parameters and disturbances
cites work: Q5526190
description: scientific article; zbMATH DE number 3928861