On the immersion of a discrete-time polynomial analytic system into a polynomial affine one
type: Item
instance of: scholarly article
title: On the immersion of a discrete-time polynomial analytic system into a polynomial affine one
zbMATH Open document ID: 0553.93018
DOI: 10.1016/0167-6911(83)90005-1
author: Salvatore Monaco
author: Dorothée Normand-Cyrot
published in: Systems \& Control Letters
publication date: 1983-01-01T00:00:00Z
review text: Within the class of discrete-time nonlinear systems which are polynomial with respect to the input the following problem is considered. Given a system \(\Sigma\) analytic with respect to the state, does there exist another system \(\Sigma'\) linear with respect to the state and an analytic map \(\tau\) from the state space \(R^ N\) of \(\Sigma\) to the state space \(R^{N'}\) of \(\Sigma\) ' such that for any \(x\in R^ N\) the input-output behavior of \(\Sigma\) initialized at \(x\) coincides with the input-output behaviour of \(\Sigma'\) initialized at \(x'=\tau (x)\). The authors give necessary and sufficient conditions on \(\Sigma\) for the existence of such \(\Sigma'\) and \(\tau\).
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93B17
zbMATH DE Number: 3882277
zbMATH Keywords: immersion
zbMATH Keywords: discrete-time nonlinear systems
zbMATH Keywords: input-output behavior
MaRDI profile type: Publication
full work available at URL: 0167-6911(83)90005-1
OpenAlex ID: W2065867627
cites work: A Finiteness Criterion for Nonlinear Input–Output Differential Systems
cites work: Q3312094
cites work: The immersion under feedback of a multidimensional discrete-time non-linear system into a linear system
cites work: Generating series for discrete-time nonlinear systems
cites work: Associative differential operations
description: scientific article; zbMATH DE number 3882277