The rational complementarity problem

An extension of the linear complementarity problem (LCP) of mathematical pr ogramming is the so-called rational complementarity problem (RCP). This pro blem occurs if complementarity conditions are imposed on input and output v ariables of linear dynamical input/state/output systems. The resulting dyna mical systems are called linear complementarity systems. Since the RCP is c rucial both in issues concerning existence and uniqueness of solutions to c omplementarity systems and in time simulation of complementarity systems, i t is worthwhile to consider existence and uniqueness questions of solutions to the RCP. In this paper necessary and sufficient conditions are presente d 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 solu tions to linear mechanical systems with unilateral constraints, electrical networks with diodes, and linear dynamical systems subject to relays and/or Coulomb friction. (C) 1999 Elsevier Science Inc. All rights reserved.