Universal \(\lambda\)-tracking for nonlinearly-perturbed systems without restrictions on the relative degree
type: Item
instance of: scholarly article
title: Universal \(\lambda\)-tracking for nonlinearly-perturbed systems without restrictions on the relative degree
zbMATH Open document ID: 0947.93025
DOI: 10.1016/S0005-1098(98)00135-6
author: Ye Xudong
published in: Automatica
publication date: 2000-11-02T00:00:00Z
review text: This paper considers an adaptive tracking problem for a class of nonlinear perturbed linear single-input single-output minimum-phase systems \((A,b,c; f)\), where \((A,b,c)\) is a state-space realization of the underlying linear system and \(f\) denotes the nonlinear perturbation. The relative degree of \((A,b,c)\) may be arbitrary, but is assumed to be known. The nonlinear perturbation \(f\) satisfies \[ \|f(t,x)\|\leq \alpha(1+|cx|^q)\quad\text{for all }x\text{ and almost all }t, \] where \(\alpha> 0\) and \(q\) is a known positive integer. Given \(\lambda>0\), a high-gain control strategy is given which guarantees that for all reference signals and all output noise signals in \(W^{1,\infty}\), the tracking error approaches the interval \([-\lambda, \lambda]\).
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 1325712
zbMATH Keywords: adaptive tracking
zbMATH Keywords: nonlinear perturbation
zbMATH Keywords: high-gain
zbMATH Keywords: tracking
reviewed by: H. Logemann
MaRDI profile type: Publication
full work available at URL: s0005-1098(98)00135-6
OpenAlex ID: W2045283708
description: scientific article; zbMATH DE number 1325712