Continuous state representations for AR systems
type: Item
instance of: scholarly article
title: Continuous state representations for AR systems
zbMATH Open document ID: 0923.93011
DOI: 10.1007/BF01212368
author: Heide Gluesing-Luerssen
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1999-10-19T00:00:00Z
review text: The behavioral setting is used to study the subclass of time-invariant, discrete-time, linear, finite-dimensional systems which can be represented by autoregressive (AR) equations over the time-axis \(\mathbb Z\). For these systems, continuity properties of realizations with respect to the parameters of the system are studied. The question investigated is: ``Under which conditions does a convergent sequence of AR-systems given by matrices \(R^{l} \in \mathbb R [s]^{p \times q}, l \in {\mathbb {\overline N}} := {\mathbb N} \cup \{ \infty \}\) have a converging sequence of input-state-output (i/s/o) representations \((A^{l}, B^{l}, C^{l}, D^{l})\)?'' It is shown that, with respect to the convergence of all coefficients in an AR representation, there exist continuously dependent (i/s/o) representations provided a specified condition on the degree of some matrix \(Q\) is satisfied. This continuous (i/s/o) representation is given by the Fuhrmann realization. These results are shown to generalize various known results. The paper is concluded with an example.
reviewed by: Frieda Theron
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 828268
zbMATH Keywords: linear systems
zbMATH Keywords: realization theory
zbMATH Keywords: behavorial approach
zbMATH Keywords: AR systems
zbMATH Keywords: polynomial matrix representations
zbMATH Keywords: continuous systems
MaRDI profile type: Publication
cites work: Q3905961
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full work available at URL: https://doi.org/10.1007/bf01212368
OpenAlex ID: W2400703361
description: scientific article; zbMATH DE number 828268