Structural controllability and observability
type: Item
instance of: scholarly article
title: Structural controllability and observability
zbMATH Open document ID: 0611.93003
DOI: 10.1016/0167-6911(86)90023-X
author: B. George
published in: Systems \& Control Letters
publication date: 1986-01-01T00:00:00Z
review text: A system whose parameters are not fixed is said to be structurally uncontrollable (unobservable) if it is uncontrollable (unobservable) for all values of the parameters. In this paper linear time-invariant systems of the following form are considered: \(\dot x=(A_ 0+\sum^{N}_{1}\alpha_ iA_ i)x+(B_ 0+\sum^{M}_{1}\beta_ iB_ i)u\), \(y=(C_ 0+\sum^{K}_{1}\gamma_ iC_ i)x\), where \(A_ 0\), \(B_ 0\), \(C_ 0\) are the nominal system parameter matrices, \(\alpha_ i\), \(\beta_ i\), \(\gamma_ i\) are the parameter variations, \(A_ i\), \(B_ i\), \(C_ i\) are matrices of rank one modelling the structure of the variations. The main results consist in necessary and sufficient conditions for a system of the above kind to be structurally uncontrollable (unobservable). When the matrices \(A_ i\), \(B_ i\), \(C_ i\) are of rank greater than one these conditions are only sufficient to assure structural uncontrollability. The criteria are illustrated by a few examples.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 3989177
zbMATH Keywords: linear time-invariant systems
zbMATH Keywords: necessary and sufficient conditions
zbMATH Keywords: structural uncontrollability
zbMATH Keywords: time-invariant
reviewed by: A. M. Perdon
MaRDI profile type: Publication
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full work available at URL: 0167-6911(86)90023-x
OpenAlex ID: W2030731250
description: scientific article; zbMATH DE number 3989177