Controllability and observability criteria for linear piecewise constant impulsive systems
type: Item
instance of: scholarly article
title: Controllability and observability criteria for linear piecewise constant impulsive systems
zbMATH Open document ID: 1251.93038
DOI: 10.1155/2012/182040
author: Hong Shi
author: Guangming Xie
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: Impulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper studies the controllability and observability of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 6106134
zbMATH Keywords: linear piecewise constant impulsive systems
zbMATH Keywords: controllability criteria
zbMATH Keywords: observability criteria
Wikidata QID: Q58905838
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/182040
OpenAlex ID: W2098478475
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DBLP publication ID: journals/jam/ShiX12
description: scientific article; zbMATH DE number 6106134