Bohl-Perron type stability theorems for linear singular difference equations
type: Item
instance of: scholarly article
title: Bohl-Perron type stability theorems for linear singular difference equations
zbMATH Open document ID: 1406.39022
author: Vu Hoang Linh
author: Ngo Thi Thanh Nga
published in: Vietnam Journal of Mathematics
publication date: 2018-07-31T00:00:00Z
review text: The paper deals with the linear singular difference equation \[ E_n y(n+1) = A_n y(n) + q_n, \qquad n = n_0,n_0 + 1,\dots, \] where \(q_n \in \mathbb R^d,\) \(E_n\) and \(A_n\) are \(d \times d\)-matrices, \({\mathrm{rank}} (E_n) = r = {\mathrm{const}} < d\) for all \(n \geq n_0.\) Using a projector-based approach the authors define the Cauchy operator associated with the corresponding homogeneous system and give definitions of stability and exponential stability. The authors prove three Bohi-Perron type theorems about the relation between the exponential stability of homogeneous system and the boundedness of solutions of the considered system.
reviewed by: Victor I. Tkachenko
Mathematics Subject Classification ID: 39A30
Mathematics Subject Classification ID: 39A06
Mathematics Subject Classification ID: 39A22
zbMATH DE Number: 6911881
zbMATH Keywords: linear singular difference equation
zbMATH Keywords: exponential stability
zbMATH Keywords: boundedness of solutions
MaRDI profile type: Publication
full work available at URL: s10013-017-0245-z
OpenAlex ID: W2605159749
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DOI: 10.1007/S10013-017-0245-Z
description: scientific article; zbMATH DE number 6911881