### 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 language | English |
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Pages (from-to) | 93-135 |

Number of pages | 43 |

Journal | Linear Algebra and Its Applications |

Volume | 294 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 1999 |

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## Cite this

Heemels, W. P. M. H., Schumacher, J. M., & Weiland, S. (1999). The rational complementarity problem.

*Linear Algebra and Its Applications*,*294*(1-3), 93-135. https://doi.org/10.1016/S0024-3795(99)00060-9