PDEs with distributed control and delay in the loop: Transfer function poles, exponential modes and robustness of stability
type: Item
instance of: scholarly article
title: PDEs with distributed control and delay in the loop: Transfer function poles, exponential modes and robustness of stability
zbMATH Open document ID: 0928.93023
DOI: 10.1016/S0947-3580(98)70126-8
author: H. Logemann
author: Richard Rebarber
published in: European Journal of Control
publication date: 1999-05-02T00:00:00Z
review text: The following distributed parameter system with distributed control and a delay in the feedback loop \[ \sum^i_{j= 0} a^k_j(x) p^k_j(D_x){\partial^j\over \partial t^j} w(x,t)= \sum^i_{j= 0} b^k_j(x){\partial^j\over \partial t^j} v(t)- \sum^i_{j= 0} b^k_j(x){\partial^j \over \partial t^j} (Cw)(t-\varepsilon), \] \[ x\in I_k,\quad t>0 \] is considered and a stability result is obtained which is independent of the delay for small delays. It is required that \[ \gamma(H)= \limsup_{| s|\to\infty}| H(s)|< 1 \] (taken to avoid the poles of \(H\)), where \(H\) is the transfer function of the system.
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93B55
Mathematics Subject Classification ID: 93D25
zbMATH DE Number: 1282230
zbMATH Keywords: robust stability
zbMATH Keywords: distributed parameter system
zbMATH Keywords: distributed control
zbMATH Keywords: delay
reviewed by: S. P. Banks
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1282230