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Lossless and dissipative distributed systems

DSpace at IIT Bombay

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Field Value
 
Title Lossless and dissipative distributed systems
 
Creator PILLAI, HK
WILLEMS, JC
 
Subject dynamical scattering systems
spectral factorization
quadratic differential forms
linear multidimensional systems
behavioral theory
polynomial matrices
lossless systems
positivity
dissipativeness
storage functions
 
Description This paper deals with linear shift-invariant distributed systems. By this we mean systems described by constant coefficient linear partial differential equations. e de ne dissipativity with respect to a quadratic differential form, i.e., a quadratic functional in the system variables and their partial derivatives. The main result states the equivalence of dissipativity and the existence of a storage function or a dissipation rate. The proof of this result involves the construction of the dissipation rate. e show that this problem can be reduced to Hilbert's 17th problem on the representation of a nonnegative rational function as a sum of squares of rational functions.
 
Publisher SIAM PUBLICATIONS
 
Date 2011-08-29T05:16:31Z
2011-12-26T12:58:25Z
2011-12-27T05:48:20Z
2011-08-29T05:16:31Z
2011-12-26T12:58:25Z
2011-12-27T05:48:20Z
2002
 
Type Article
 
Identifier SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 40(5), 1406-1430
0363-0129
http://dx.doi.org/10.1137/S0363012900368028
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11972
http://hdl.handle.net/10054/11972
 
Language en