Destabilizing effects of small time delays on feedback-controlled descriptor systems
type: Item
instance of: scholarly article
title: Destabilizing effects of small time delays on feedback-controlled descriptor systems
zbMATH Open document ID: 0986.93056
DOI: 10.1016/S0024-3795(97)00328-5
published in: Linear Algebra and its Applications
publication date: 2002-06-13T00:00:00Z
review text: The following controlled descriptor system is considered \[ E\dot x(t)= Ax(t)+ Bu(t).\tag{1} \] Under certain conditions the following result is obtained: there exist sequences \((\varepsilon_j)\) and \((s_j)\) with \(\varepsilon_j> 0\), \(\varepsilon_j\to 0\), \(s_j\in \{s\in\mathbb{C}\mid\text{Re }s> 0\}\), \(\text{Im }\varepsilon_j\to \infty\), \(\text{Re }s_j\to \infty\), such that for any \(j\in \mathbb{N}\) the system (1) with a delayed feedback control \[ u(t)= Fx(t- \varepsilon_j)\tag{2} \] has the solution \[ x_j(t)= e^{s_jt} x_0,\quad x_0\neq 0, \] i.e., the system (1) with a feedback (2) is non-stable. Some examples are presented.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 34A09
zbMATH DE Number: 1116066
zbMATH Keywords: destabilizing feedback
zbMATH Keywords: descriptor system
zbMATH Keywords: delayed feedback
author: H. Logemann
reviewed by: T. Tadumadze
MaRDI profile type: Publication
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Wikidata QID: Q127442631
description: scientific article; zbMATH DE number 1116066