A behavioral approach to singular systems
type: Item
instance of: scholarly article
title: A behavioral approach to singular systems
zbMATH Open document ID: 0916.93008
DOI: 10.1023/A:1006106222280
author: Vakhtang Lomadze
author: M. S. Ravi
author: Joachim Rosenthal
author: Johannes M. Schumacher
published in: Acta Applicandae Mathematicae
publication date: 1999-07-12T00:00:00Z
review text: The behavioral approach to linear systems has received a great deal of attention since it was first introduced by \textit{J. C. Willems} [Automatica 22, 561-580 (1986; Zbl 0604.62090)]. In the present paper, abstract linear behaviors are defined as generalization of Willems' behaviors. This new notion allows a description of singular systems in a very natural way. It is shown that there is a one-to-one correspondence between the class of abstract linear behaviors and coherent sheaves on the projective line. Realization theory is studied in this setting and the paper ends with definitions of controllability and observability based on abstract linear behaviors.
Mathematics Subject Classification ID: 93A05
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 1267837
zbMATH Keywords: singular systems
zbMATH Keywords: shift spaces
zbMATH Keywords: coherent sheaves
zbMATH Keywords: realization
zbMATH Keywords: abstract linear behaviors
reviewed by: Frieda Theron
MaRDI profile type: Publication
full work available at URL: a:1006106222280
OpenAlex ID: W2113356353
description: scientific article; zbMATH DE number 1267837