First-order representations of delay-differential systems in a behavioural setting
type: Item
instance of: scholarly article
title: First-order representations of delay-differential systems in a behavioural setting
zbMATH Open document ID: 0886.93010
DOI: 10.1016/S0947-3580(97)70072-4
published in: European Journal of Control
publication date: 1998-04-21T00:00:00Z
review text: Consider the behaviour \(B=\ker R\) where the matrix \(R\) of delay-differential operators belongs to \(\mathbb{R} [d/dt,\sigma]^{p \times k}\) and \(\sigma\) denotes the forward shift. The purpose of this paper is to find matrices, \(A\), \(B\), \(C\) and \(D\) of appropriate sizes and a permutation matrix \(\rho\) such that \[ \ker R=B= \left\{\rho {u \choose y} \bigl|\text{ there exists a trajectory } x: \begin{matrix} \dot x & = Ax & + Bu \\ y & = Cx & + Du \end{matrix} \right\}. \] Commensurate point-delays are allowed so that the system is over the ring \(\mathbb{R} [\sigma]\). The matrices \(A\), \(B\), \(C\) and \(D\) have delay operators as entries. Such a system \(\dot x=Ax +Bu\), \(y= Cx+Du\) is called a realization of the behaviour. Necessary and sufficient conditions for the realizability as first-order systems of behaviours are derived. A realization procedure is performed.
reviewed by: Jingbo Wu
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93B25
zbMATH DE Number: 1063884
zbMATH Keywords: behaviour
zbMATH Keywords: delay-differential operators
zbMATH Keywords: realization
author: Heide Gluesing-Luerssen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1063884