The extended linear complementarity problem and linear complementary-slackness systems

First we introduce the Extended Linear Complementarity Problem, which is a kind of mathematical programming problem. Next we show how this problem arises when we want to compute stationary points of linear complementary-slackness systems or when we want to determine the uniqueness of smooth continuations and the associated mode selection problem for linear complementary-slackness systems. We also briefly discuss the role of the Extended Linear Complementarity Problem in the analysis of other classes of hybrid systems such as discrete event systems and traffic signal controlled intersections.