State reconstruction of the wave equation with general viscosity and non-collocated observation and control
type: Item
instance of: scholarly article
title: State reconstruction of the wave equation with general viscosity and non-collocated observation and control
zbMATH Open document ID: 1467.93155
author: Fu Zheng
author: Hao Zhou
published in: Journal of Mathematical Analysis and Applications
publication date: 2021-06-14T00:00:00Z
review text: It is considered the problem of reconstructing the initial condition (state) for the input-state-output \(1D\) system with distributed parameters described by hyperbolic partial differential equation and controlled/observed boundary conditions \[ \displaylines{\displaystyle{y_{tt} - y_{xx} + a(x)y_t = 0\ ;\ 0<x<1\;,\;t>0}\cr \displaystyle{y(0,t) = 0\ ,\ y_x(1,t) = u(t)}\cr O(t) = y_x(0,t)} \] The problem is solved in terms of Luenberger observers, requiring analysis of stability and stabilization of the above system. Stabilization is achieved by local feedback \(u(t)=\alpha y_t(1,t)\) The paper also makes use of the approximation based on the method of lines.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 93D23
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65N40
zbMATH DE Number: 7358723
zbMATH Keywords: wave equation
zbMATH Keywords: non-collocated observation and control
zbMATH Keywords: exponential stability
zbMATH Keywords: state reconstruction
zbMATH Keywords: semi-discretization
MaRDI profile type: Publication
full work available at URL: j.jmaa.2021.125257
OpenAlex ID: W3155357442
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DOI: 10.1016/J.JMAA.2021.125257
description: scientific article; zbMATH DE number 7358723