Stability of multidimensional nonnegative systems
type: Item
instance of: scholarly article
title: Stability of multidimensional nonnegative systems
zbMATH Open document ID: 0962.93077
DOI: 10.1007/BF01204574
author: Tatsushi Ooba
published in: Circuits, Systems, and Signal Processing
publication date: 2001-06-18T00:00:00Z
review text: The stability of the linear mD system \[ x(i) =\sum^m_{l=1} A_lx(i- e_l), \] where \(x(i)\in \mathbb{R}^n\), \(A_l\in \mathbb{R}^{n\times n}\), \(i= (i_1,\dots, i_m)\), \(i- e_l= (i_1,\dots, i_l- 1,\dots, i_m)\) is analyzed by the use of a localized Lyapunov function. It is shown that if the spectral radius of \(B= \sum^m_{l= 1}|A_l|\), \(\rho(B)<1\), then the system is diagonally strongly stable and any state transition of the system decreases step-by-step with respect to an appropriately constructed localized diagonal Lyapunov function. It is an extension of a known result on the stability of nonnegative matrices.
reviewed by: Tadeusz Kaczorek
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 1513149
zbMATH Keywords: asymptotic stability
zbMATH Keywords: discrete systems
zbMATH Keywords: linear mD system
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1513149