Canonical correlations of past inputs and future outputs for linear stochastic systems
type: Item
instance of: scholarly article
title: Canonical correlations of past inputs and future outputs for linear stochastic systems
zbMATH Open document ID: 0545.93012
DOI: 10.1016/S0167-6911(84)80027-4
author: Michele Pavon
published in: Systems \& Control Letters
publication date: 1984-01-01T00:00:00Z
review text: The paper deals with the dependence of future outputs on past inputs via canonical correlation analysis. One considers here a discrete-time stochastic system described by the state difference equation \(x(t+1)=Ax(t)+Bu(t)\) and the output equation \(y(t)=Cx(t)+Du(t)\) where A, B, C and D are constant matrices and the input u(t) is a normalized p- dimensional Gaussian white-noise. The author takes advantage of the fact that the usual notions of dependence between Gaussian processes can be reduced to geometric conditions which in turn can be expressed in terms of canonical correlation coefficients to focus on the characterization of these coefficients by means of system-theoretic quantities. Finally, the author indicates, how her results can be applied to the problem of approximating stochastic systems through lower-dimensional systems.
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 62J99
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93B20
zbMATH DE Number: 3869134
zbMATH Keywords: stochastic realization
zbMATH Keywords: canonical correlation analysis
reviewed by: Guillermo I. Gómez
MaRDI profile type: Publication
cites work: Infinite Hankel block matrices and related extension problems
cites work: Stochastic theory of minimal realization
cites work: Markovian Representation of Stochastic Processes by Canonical Variables
cites work: A stochastic realization approach to the smoothing problem
cites work: Q3859622
cites work: Calculation of the amount of information about a random function contained in another such function
cites work: Q3243448
cites work: Q4174025
cites work: Canonical correlations of past and future for time series: Definitions and theory
cites work: Canonical correlations of past and future for time series: Bounds and computation
cites work: Q5529067
cites work: Optimal Hankel-norm model reductions: Multivariable systems
cites work: Stochastic Realization and Invariant Directions of the Matrix Riccati Equation
cites work: Q3908070
cites work: Hankel operators, best approximations, and stationary Gaussian processes
cites work: Q5531487
cites work: Q4169482
full work available at URL: s0167-6911(84)80027-4
OpenAlex ID: W2039236897
description: scientific article; zbMATH DE number 3869134