Minimal representations of implicit linear systems
type: Item
instance of: scholarly article
title: Minimal representations of implicit linear systems
zbMATH Open document ID: 0565.93012
DOI: 10.1016/0005-1098(85)90059-7
author: J. D. Aplevich
published in: Automatica
publication date: 1985-01-01T00:00:00Z
review text: The paper investigates a generalized linear system description with the purpose i) to establish a set of simple conditions necessary and sufficient for the linear system model to be minimal in a certain well- defined sense, and ii) to set up a stable algorithm for deriving a minimal representation from a non-minimal one. The conditions for minimality are formulated in four properties concerning row- as well as column regularities of matrices which form the partitioned coefficient matrix of the associated homogeneous linear system. So, four rank tests are needed to check minimality. Two of them correspond to generalizations of controllability and observability criteria, the third one corresponds to removal of system poles at infinity, and the last one takes into account the set of algebraically dependent variables. For linear state-space models two of the four criteria are always valid. The four steps in the minimization algorithm correspond to the four properties necessary for minimality. A pseudo- algorithmic language is used for description of the procedures. They are tested in an illustrative numerical example.
Mathematics Subject Classification ID: 93B20
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 34A99
Mathematics Subject Classification ID: 65J10
zbMATH DE Number: 3902476
zbMATH Keywords: generalized linear system
zbMATH Keywords: minimal representation
zbMATH Keywords: rank tests
zbMATH Keywords: linear state-space models
zbMATH Keywords: minimization algorithm
describes a project that uses: LINPACK
MaRDI profile type: Publication
full work available at URL: 0005-1098(85)90059-7
OpenAlex ID: W2409149964
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description: scientific article; zbMATH DE number 3902476