The rational complementarity problem Original Research Article

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 sufficient 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.