Impedance passive and conservative boundary control systems
type: Item
instance of: scholarly article
title: Impedance passive and conservative boundary control systems
zbMATH Open document ID: 1134.47059
author: Jarmo Malinen
author: Olof Staffans
published in: Complex Analysis and Operator Theory
publication date: 2007-08-10T00:00:00Z
review text: The external Cayley transform is used for the conversion between the linear dynamical systems in scattering form and in impedance form. This transformation is used to define a class of formal impedance conservative boundary control systems (colligations), without assuming a priori that the associated Cauchy problems are solvable. Sufficient and necessary conditions are developed guaranteeing that impedance conservative colligations are internally well-posed boundary nodes, that is, the associated Cauchy problems are solvable and governed by \(C_0\)-semigroups. Further, a ``strong'' variant of colligations is defined and it is shown that ``strong'' impedance conservative boundary colligations are a slight generalization of the ``abstract boundary space'' construction for symmetric operators. Examples, involving the transmission line and the wave equations, are illustrating the obtained results.
reviewed by: Birgit Jacob
Mathematics Subject Classification ID: 47N70
Mathematics Subject Classification ID: 47A48
Mathematics Subject Classification ID: 35R20
Mathematics Subject Classification ID: 93C25
zbMATH DE Number: 5178720
zbMATH Keywords: passive systems
zbMATH Keywords: impedance
zbMATH Keywords: scattering
zbMATH Keywords: boundary node
zbMATH Keywords: well-posedness
zbMATH Keywords: contraction semigroup
zbMATH Keywords: abstract boundary space
MaRDI profile type: Publication
full work available at URL: s11785-006-0009-3
OpenAlex ID: W2000566727
DOI: 10.1007/S11785-006-0009-3
description: scientific article; zbMATH DE number 5178720