Abstract
Original language | English |
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Pages (from-to) | 397-420 |
Journal | Mathematical Programming |
Volume | 157 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jun 2016 |
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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
TY - JOUR
T1 - Linear passive systems and maximal monotone mappings
AU - Camlibel, M.K.
AU - Schumacher, Hans
PY - 2016/6/1
Y1 - 2016/6/1
N2 - 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.
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.
U2 - 10.1007/s10107-015-0945-7
DO - 10.1007/s10107-015-0945-7
M3 - Article
VL - 157
SP - 397
EP - 420
JO - Mathematical Programming
JF - Mathematical Programming
SN - 0025-5610
IS - 2
ER -