Controllability and observability of time-invariant linear dynamic systems.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1265.34334
author: Nick Wintz
author: Martin Bohner
publication date: 2012-10-08T00:00:00Z
full work available at URL: https://eudml.org/doc/246984
full work available at URL: mb137-2
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 6092234
zbMATH Keywords: time scale
zbMATH Keywords: dynamic equation
zbMATH Keywords: controllability
zbMATH Keywords: reachability
zbMATH Keywords: observability
zbMATH Keywords: duality principle
MaRDI profile type: Publication
OpenAlex ID: W2143183467
DOI: 10.21136/MB.2012.142861
title: Controllability and observability of time-invariant linear dynamic systems.
published in: Mathematica Bohemica
review text: The paper is concerned with linear dynamic time-invariant control systems of the forms NEWLINE\[NEWLINEx^{\Delta }(t)=-Ax^{\sigma }(t)+Bu(t),\;\;\;y(t)=Cx^{\sigma }(t),\tag{1}NEWLINE\]NEWLINE where \(x\), \(y\), \(u\) denote the state, input, and output of the system, respectively. It is assumed that \(u\) is an rd-continuous function, and \(A\) is a regressive matrix.NEWLINENEWLINEThe authors derive necessary and sufficient conditions for the controllability and reachability of system (1), which generalize the usual ones which are well known in the classical control theory.NEWLINENEWLINEThe final result is a duality theorem, which says that the controllability of (1) is equivalent to the observability of NEWLINE\[NEWLINEx^{\Delta }(t)=A^T x(t)+C^T u(t),\;\;\;y(t)=B^T x(t).NEWLINE\]
reviewed by: Antonín Slavík
description: scientific article; zbMATH DE number 6092234