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Linear passive systems and maximal monotone mappings

Camlibel, M. K. & Schumacher, J. M. Jun-2016 In : Mathematical Programming. 157, 2, p. 397-420 24 p.

Research output: Scientific - peer-reviewArticle

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DOI

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.

Original languageEnglish
Pages (from-to)397-420
Number of pages24
JournalMathematical Programming
Volume157
Issue number2
StatePublished - Jun-2016

    Keywords

  • DYNAMICAL-SYSTEMS, COMPLEMENTARITY SYSTEMS, VARIATIONAL-INEQUALITIES, DIFFERENTIAL-INCLUSIONS, ABSOLUTE STABILITY, RELAY SYSTEMS, UNIQUENESS, NETWORKS

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