Null controllability of nonlinear infinite delay systems with time varying multiple delays in control
type: Item
instance of: scholarly article
title: Null controllability of nonlinear infinite delay systems with time varying multiple delays in control
zbMATH Open document ID: 0856.93011
DOI: 10.1016/0893-9659(96)00042-0
published in: Applied Mathematics Letters
publication date: 1997-02-25T00:00:00Z
review text: Nonlinear time-varying control systems with time-varying infinite multiple delays in the control are considered. Using Schauder's fixed point theorem for nonlinear mappings in Banach spaces, a sufficient condition for relative null-controllability in a given time interval is formulated and proved. More precisely, it is shown that if the uncontrolled dynamical system is uniformly asymptotically stable, and if the linear nonperturbed system is relative null-controllable, then the nonlinear infinite delay system is relative null-controllable. Moreover, some remarks and comments on relative controllability for dynamical systems with delays in the control are given. Thus, theorems presented by the reviewer [\textit{J. Klamka}, Int. J. Control 24, 869-878 (1976; Zbl 0342.93006)], where systems with multiple finite delays in the control were considered, are extended here to infinite delay controllability.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 34K35
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 915106
zbMATH Keywords: nonlinear
zbMATH Keywords: time-varying
zbMATH Keywords: infinite multiple delays
zbMATH Keywords: Schauder fixed point theorem
zbMATH Keywords: null-controllable
zbMATH Keywords: relative controllability
author: Krishnan Balachandran
author: J. P. Dauer
reviewed by: Jerzy Klamka
MaRDI profile type: Publication
full work available at URL: 0893-9659(96)00042-0
OpenAlex ID: W2029621641
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description: scientific article; zbMATH DE number 915106