Robustness of nonlinear delay equations with respect to input perturbations: a trajectory-based approach.
type: Item
instance of: scholarly article
title: Robustness of nonlinear delay equations with respect to input perturbations: a trajectory-based approach.
zbMATH Open document ID: 1069.93037
author: Luc Moreau
author: Wim Michiels
author: D. Aeyels
author: Dirk Roose
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 2002-01-01T00:00:00Z
review text: The authors study the effects of input perturbations \(\eta\) on the stability properties of the delay differential equation (DDE) \[ \dot x(t)=f(t,x(t),x(t-\tau))+\psi(t,x(t),x(t-\tau))\eta(t), \] under the assumptions that the unperturbed DDE \(\dot x(t)=f(t,x(t),x(t-\tau))\) has a globally uniformly asymptotically stable null-solution. Although stability results for delay differential equations are usually obtained within a Lyapunov framework, they study stability and boundedness properties by means of an alternative approach, which is based on an analysis of trajectories by means of the Gronwall Lemma. This alternative approach may be seen as an extension of the trajectory-based approach developed e.g. in [\textit{L. Moreau} and \textit{D. Aeyels}, SIAM J. Control Optimization 41, No. 6, 1922--1945 (2003; Zbl 1054.34084)] for ordinary differential equations to delay differential equations. Within this framework they have generalized some stability and boundedness results from [\textit{W. Michiels, R. Sepulchre} and \textit{D. Roose}, SIAM J. Control Optimization 40, No. 3, 661--680 (2001; Zbl 1002.34069)] to a much broader class of delay differential equations.
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 1890503
zbMATH Keywords: Nonlinear delay equations
zbMATH Keywords: stability
zbMATH Keywords: perturbations
zbMATH Keywords: trajectory-based approach
zbMATH Keywords: cascade systems
reviewed by: Pavel Rehak
MaRDI profile type: Publication
full work available at URL: s004980200013
OpenAlex ID: W2056894041
DOI: 10.1007/S004980200013
description: scientific article; zbMATH DE number 1890503