Mode Selection in Linear Complementarity Systems

Abstract

In this paper, the object of study is the class of 'linear complementarity systems' given by differential equations and inequalities similar as in the Linear Complementarity Problem of mathematical programming. In the description of the evolution of such systems, a key role is played by the set of inequalities that hold with equality. These sets determine the so-called 'modes.' Three equivalent mode selection methods are presented that specify the mode given the continuous state of the system. Finally, a sufficient condition for (local) existence and uniqueness of a solution to linear complementarity systems is presented.