On the stability of some systems with aftereffect
type: Item
instance of: scholarly article
title: On the stability of some systems with aftereffect
zbMATH Open document ID: 0823.93055
author: V. B. Kolmanovskii
published in: Automation and Remote Control
publication date: 1995-02-19T00:00:00Z
review text: A method of constructing Lyapunov functionals for some systems with an arbitrary aftereffect is suggested. Such an aftereffect may be observed in models for biotechnical systems -- an example treated in the paper --, where the actual growth rate of microorganisms may be not only dependent on the actually available substrate concentration but also on the recent history of this state variable. The method is developed for linear systems and then extended to certain nonlinear systems. An interesting result lies in the remark that for some systems, the aftereffect seems to be necessary for their stabilization.
Mathematics Subject Classification ID: 93D30
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 34K35
zbMATH DE Number: 710827
zbMATH Keywords: delay
zbMATH Keywords: Lyapunov functionals
zbMATH Keywords: aftereffect
zbMATH Keywords: stabilization
reviewed by: Axel Munack
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 710827