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 in	Mathematical programming Vol. 157; no. 2; pp. 397 - 420
Main Authors	Camlibel, M. K., Schumacher, J. M.
Format	Journal Article
Language	English
Published	Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2016 Springer Nature B.V
Subjects	Calculus of Variations and Optimal Control; Optimization Collaboration Combinatorics Convex analysis Differential equations Dynamical systems Full Length Paper Inclusions Interconnection Linear systems Mapping Mathematical analysis Mathematical and Computational Physics Mathematical functions Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Partial differential equations Passivity Studies System theory Theoretical Uniqueness 47H05 93C05 34A60 34A12 90C33 47H04
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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.
AbstractList	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. Issue Title: Special Issue: Complementarity Problems and Applications 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.
Author	Schumacher, J. M. Camlibel, M. K.
Author_xml	– sequence: 1 givenname: M. K. surname: Camlibel fullname: Camlibel, M. K. email: m.k.camlibel@rug.nl organization: Department of Mathematics, University of Groningen, Department of Electronics and Communication Engineering, Dogus University – sequence: 2 givenname: J. M. surname: Schumacher fullname: Schumacher, J. M. organization: Department of Econometrics and Operations Research, Tilburg University
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Cites_doi	10.1016/0022-1236(69)90032-9 10.1007/s10107-006-0052-x 10.1098/rspa.1960.0144 10.1109/9.664151 10.1016/S0024-3795(01)00593-6 10.1137/S0036139997325199 10.3166/ejc.8.220-237 10.1016/S0167-6377(00)00042-0 10.1016/S0005-1098(98)90177-7 10.1109/TPEL.2008.2007420 10.1109/TAC.2004.825654 10.1007/s11228-007-0051-y 10.1007/s00033-012-0276-y 10.1007/s10107-013-0678-4 10.2140/pjm.1970.33.209 10.1109/TCSI.2003.815195 10.1137/0131050 10.1134/S0005117906100043 10.1016/j.sysconle.2003.09.007 10.1109/81.989165 10.1016/j.na.2010.08.034 10.1016/S0005-1098(03)00237-1 10.1307/mmj/1028998564 10.1016/S0021-7824(03)00071-0 10.1007/s00498-004-0145-0 10.1515/9781400873173 10.1137/1.9781611970715 10.1051/m2an:2002020 10.1007/978-1-4471-0339-4 10.1007/s10107-009-0268-7 10.1007/s10107-004-0544-5
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Snippet	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... Issue Title: Special Issue: Complementarity Problems and Applications This paper deals with a class of dynamical systems obtained from interconnecting linear...
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SubjectTerms	Calculus of Variations and Optimal Control; Optimization Collaboration Combinatorics Convex analysis Differential equations Dynamical systems Full Length Paper Inclusions Interconnection Linear systems Mapping Mathematical analysis Mathematical and Computational Physics Mathematical functions Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Partial differential equations Passivity Studies System theory Theoretical Uniqueness
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Title	Linear passive systems and maximal monotone mappings
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