On the positive orthant controllability of two-dimensional bilinear systems
type: Item
instance of: scholarly article
title: On the positive orthant controllability of two-dimensional bilinear systems
zbMATH Open document ID: 0532.93005
DOI: 10.1016/0167-6911(83)90038-5
author: Andrea Bacciotti
published in: Systems \& Control Letters
publication date: 1983-01-01T00:00:00Z
review text: In the paper complete controllability on the positive orthant \(M=\{x\in R^ 2:x_ 1>0,\quad x_ 2>0\}\) of two-dimensional stationary bilinar control systems \[ \dot x(t)=(A+u(t)B)x(t),\quad x(t)\in M \] is considered. It is assumed, that the 2\(\times 2\) matrix A is essentially positive, that is \(a_{12}>0\), \(a_{21}>0\), and moreover, B is a 2\(\times 2\) diagonal matrix with nonzero diagonal elements \(b_ 1\neq 0,b_ 2\neq 0.\) Using the general results formulated in a paper of \textit{W. M. Boothby} [SIAM J. Control Optimization 20, 634-644 (1982; Zbl 0488.93009)], sufficient and necessary conditions for complete controllability on the positive orthant M are presented. Some additional comments concerning more general multi-dimensional bilinear stationary control systems are also given.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C99
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 3845421
zbMATH Keywords: complete controllability
zbMATH Keywords: bilinear systems
zbMATH Keywords: unbounded controls
zbMATH Keywords: positive orthant
reviewed by: Jerzy Klamka
MaRDI profile type: Publication
full work available at URL: 0167-6911(83)90038-5
OpenAlex ID: W2025395930
cites work: The region of attainability of nonlinear systems with unbounded controls
cites work: On the relationship between global and local controllability
cites work: Some Comments on Positive Orthant Controllability of Bilinear Systems
cites work: Controllability of general nonlinear systems
cites work: Global controllability of nonlinear systems in two dimensions
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description: scientific article; zbMATH DE number 3845421