The rational complementarity problem

W.P.M.H. Heemels, J.M. Schumacher, S. Weiland

Research output: Contribution to journalArticleAcademicpeer-review

33 Citations (Scopus)

Abstract

An extension of the linear complementarity problem (LCP) of mathematical programming is the so-called rational complementarity problem (RCP). This problem occurs if complementarity conditions are imposed on input and output variables of linear dynamical input/state/output systems. The resulting dynamical systems are called linear complementarity systems. Since the RCP is crucial both in issues concerning existence and uniqueness of solutions to complementarity systems and in time simulation of complementarity systems, it is worthwhile to consider existence and uniqueness questions of solutions to the RCP. In this paper necessary and su�cient conditions are presented guaranteeing existence and uniqueness of solutions to the RCP in terms of corresponding LCPs. Using these results and proving that the corresponding LCPs have certain properties, we can show uniqueness and existence of solutions to linear mechanical systems with unilateral constraints, electrical networks with diodes, and linear dynamical systems subject to relays and/or Coulomb friction. Ó 1999 Elsevier Science Inc. All rights reserved.
Original languageEnglish
Pages (from-to)93-135
Number of pages43
JournalLinear Algebra and Its Applications
Volume294
Issue number1-3
DOIs
Publication statusPublished - 1999

Fingerprint

Complementarity Problem
Complementarity
Dynamical systems
Diodes
Friction
Existence and Uniqueness of Solutions
Unilateral Constraint
Electrical Networks
Coulomb Friction
Output
Linear Complementarity Problem
Uniqueness of Solutions
Diode
Mechanical Systems
Relay
Dynamical system
Linear Systems
Necessary
Term

Cite this

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The rational complementarity problem. / Heemels, W.P.M.H.; Schumacher, J.M.; Weiland, S.

In: Linear Algebra and Its Applications, Vol. 294, No. 1-3, 1999, p. 93-135.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - The rational complementarity problem

AU - Heemels, W.P.M.H.

AU - Schumacher, J.M.

AU - Weiland, S.

PY - 1999

Y1 - 1999

N2 - An extension of the linear complementarity problem (LCP) of mathematical programming is the so-called rational complementarity problem (RCP). This problem occurs if complementarity conditions are imposed on input and output variables of linear dynamical input/state/output systems. The resulting dynamical systems are called linear complementarity systems. Since the RCP is crucial both in issues concerning existence and uniqueness of solutions to complementarity systems and in time simulation of complementarity systems, it is worthwhile to consider existence and uniqueness questions of solutions to the RCP. In this paper necessary and su�cient conditions are presented guaranteeing existence and uniqueness of solutions to the RCP in terms of corresponding LCPs. Using these results and proving that the corresponding LCPs have certain properties, we can show uniqueness and existence of solutions to linear mechanical systems with unilateral constraints, electrical networks with diodes, and linear dynamical systems subject to relays and/or Coulomb friction. Ó 1999 Elsevier Science Inc. All rights reserved.

AB - An extension of the linear complementarity problem (LCP) of mathematical programming is the so-called rational complementarity problem (RCP). This problem occurs if complementarity conditions are imposed on input and output variables of linear dynamical input/state/output systems. The resulting dynamical systems are called linear complementarity systems. Since the RCP is crucial both in issues concerning existence and uniqueness of solutions to complementarity systems and in time simulation of complementarity systems, it is worthwhile to consider existence and uniqueness questions of solutions to the RCP. In this paper necessary and su�cient conditions are presented guaranteeing existence and uniqueness of solutions to the RCP in terms of corresponding LCPs. Using these results and proving that the corresponding LCPs have certain properties, we can show uniqueness and existence of solutions to linear mechanical systems with unilateral constraints, electrical networks with diodes, and linear dynamical systems subject to relays and/or Coulomb friction. Ó 1999 Elsevier Science Inc. All rights reserved.

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DO - 10.1016/S0024-3795(99)00060-9

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