Realisation problem for weakly positive linear systems
type: Item
instance of: scholarly article
title: Realisation problem for weakly positive linear systems
zbMATH Open document ID: 0979.93016
author: Tadeusz Kaczorek
published in: Bulletin of the Polish Academy of Sciences. Technical Sciences
publication date: 2001-02-20T00:00:00Z
review text: The author considers a descriptor discrete-time linear system having the representation \[ Ex_{i+1}= Ax_i+ Bu_i,\quad y_i= Cx_i,\quad i\in\mathbb{Z}_+, \] where \(E,A\in \mathbb{R}^{n\times n}\), \(B\in \mathbb{R}^{n\times m}\), \(C\in \mathbb{R}^{p\times n}\), \(\text{det }E= 0\) and \(\text{det }Ez- A\neq 0\) for some \(z\in\mathbb{C}\). Such a system is called weakly positive if the matrices \(E\), \(A\), \(B\), \(C\) have nonnegative entries; in this case it is said to be a positive realization of a given rational matrix \(T(z)\in \mathbb{R}^{p\times m}(z)\) if \(T(z)= C(Ez- A)^{-1}B\). Canonical forms for weakly positive linear systems are introduced and sufficient conditions for the existence of positive realizations in canonical forms are obtained; these conditions are expressed in terms of the signs of the coefficients of the entries of \(T(z)\). Explicit formulae for the positive realizations in canonical forms are obtained.
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 1567219
zbMATH Keywords: descriptor discrete-time linear system
zbMATH Keywords: positive realization
zbMATH Keywords: weakly positive linear systems
zbMATH Keywords: canonical forms
reviewed by: Valeriu Prepeliţă
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1567219