The state-variable representation of piecewise linear functions

Abstract

A correspondence f is called a linear complementarity correspondence if it has a state-variable representation, which can be reformulated as the linear complementarity problem. The paper introduces Classes P and ULT of linear complementarity correspondences, and shows that these classes and the family of all piecewise linear functions coincide with each other. Moreover, the paper discusses the minimum dimensional state-variable representation problem, called the minimal realization problem, and introduces new concepts concerning redundancy in the state-variables.