Linear passive systems and maximal monotone mappings

M.K. Camlibel, Hans Schumacher

Research output: Contribution to journal › Article › Scientific › peer-review

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Abstract

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
JournalMathematical Programming
Volume157
Issue number2
DOIs
Publication statusPublished - 1 Jun 2016

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Maximal Monotone Mapping
Passive System
Differential Inclusions
Interconnection
Linear systems
Linear Systems
Monotone Mapping
Passivity
Set-valued Mapping
Existence and Uniqueness of Solutions
Well-posedness
Monotone
Dynamical systems
Dynamical system
Class

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Camlibel, M.K. ; Schumacher, Hans. / Linear passive systems and maximal monotone mappings. In: Mathematical Programming . 2016 ; Vol. 157, No. 2. pp. 397-420.
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Camlibel, MK & Schumacher, H 2016, 'Linear passive systems and maximal monotone mappings', Mathematical Programming , vol. 157, no. 2, pp. 397-420. https://doi.org/10.1007/s10107-015-0945-7

Linear passive systems and maximal monotone mappings. / Camlibel, M.K.; Schumacher, Hans.

In: Mathematical Programming , Vol. 157, No. 2, 01.06.2016, p. 397-420.

Research output: Contribution to journal › Article › Scientific › peer-review

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AB - 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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Camlibel MK, Schumacher H. Linear passive systems and maximal monotone mappings. Mathematical Programming . 2016 Jun 1;157(2):397-420. https://doi.org/10.1007/s10107-015-0945-7

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