Linear passive systems and maximal monotone mappings

This paper deals with a class of dynamical systems obtained from interconnecting linear systems with static set-valued relations. We first show that such an interconnection can be described by a differential inclusions with a maximal monotone set-valued mappings when the underlying linear system is...

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Published inMathematical programming Vol. 157; no. 2; pp. 397 - 420
Main Authors Camlibel, M. K., Schumacher, J. M.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2016
Springer Nature B.V
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Summary:This paper deals with a class of dynamical systems obtained from interconnecting linear systems with static set-valued relations. We first show that such an interconnection can be described by a differential inclusions with a maximal monotone set-valued mappings when the underlying linear system is passive and the static relation is maximal monotone. Based on the classical results on such differential inclusions, we conclude that such interconnections are well-posed in the sense of existence and uniqueness of solutions. Finally, we investigate conditions which guarantee well-posedness but are weaker than passivity.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-015-0945-7