On scattering passive system nodes and maximal scattering dissipative operators
Author:
Olof J. Staffans
Journal:
Proc. Amer. Math. Soc. 141 (2013), 13771383
MSC (2010):
Primary 47B44, 93A05, 93C25
Published electronically:
September 5, 2012
MathSciNet review:
3008884
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Abstract: There is an extensive literature on a class of linear timeinvariant dynamical systems called ``wellposed scattering passive systems''. Such a system is generated by an operator which is called a scattering passive system node. In the existing literature such a node is typically introduced by first giving a list of assumptions which imply that is a system node and then adding an inequality which forces this system node to be scattering passive. Here we proceed in the opposite direction: we start by requiring that satisfies the passivity inequality and then ask the question, what additional conditions are needed in order for to be a system node? The answer is surprisingly simple: A necessary and sufficient condition for an operator to be a scattering passive system node is that is closed and maximal within the class of operators that satisfy the passivity inequality. In the absence of external inputs and outputs, this condition is identical to the standard condition which characterizes the class of operators which generate contraction semigroups on Hilbert spaces.
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Additional Information
Olof J. Staffans
Affiliation:
Department of Mathematics, Åbo Akademi University, FIN20500 Åbo, Finland
DOI:
http://dx.doi.org/10.1090/S000299392012118878
Keywords:
Scattering passive,
system node,
maximally dissipative operator,
wellposed linear system
Received by editor(s):
August 20, 2011
Published electronically:
September 5, 2012
Communicated by:
Richard Rochberg
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
