Criteria for stability in approximate delay systems
type: Item
instance of: scholarly article
title: Criteria for stability in approximate delay systems
zbMATH Open document ID: 0945.34060
DOI: 10.1016/S0898-1221(99)00250-3
author: C. F. Alastruey
author: José R. González de Mendívil
author: M. De la Sen
publication date: 2000-10-03T00:00:00Z
review text: The authors consider the system of ordinary differential equations with constant delay \(\tau>0\) \[ x'(t)= Ax(t)+ Bx(t-\tau),\quad t\geq 0,\tag{1} \] and constant matrices \(A, B\in \mathbb{R}^{n\times n}\). They use some theorem on asymptotic stability due to \textit{T. Mori} [IEEE Trans. Autom. Control AC-30, 158-161 (1985; Zbl 0557.93058)]. This theorem requires solving transcendent equations and cannot be applied in real time to (1). The aim of the paper is a construction of an approximate system to (1) such that the asymptotic stability for this approximation implies the same property for (1). The asymptotic stability conditions on the approximate system are simplified and can be computed. Two examples are given.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 1429544
zbMATH Keywords: linear systems of ordinary differential equations
zbMATH Keywords: asymptotic stability
zbMATH Keywords: effective methods
Wikidata QID: Q57675785
reviewed by: Tadeusz Dłotko
MaRDI profile type: Publication
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full work available at URL: s0898-1221(99)00250-3
OpenAlex ID: W2168654618
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1429544