The rational complementarity problem (Q1124898)

An extension of the Linear Complementarity Problem (LCP) is the Rational Complementarity Problem (RCP), in which the field of real numbers is replaced by the field of rational functions with real coefficients equiped with a suitable order. This problem has relations to a class of discontinuous dynamical systems, called linear complementarity systems. The connection between RCP and a parametrized form of the LCP is explored in this paper to prove necessary and sufficient conditions for the existence and uniqueness of solutions to RCP. These results are applied to three physically relevant classes of linear complementarity systems.