When is a linear complementarity system controllable?

Abstract

This paper deals with the controllability problem of a class of piecewise linear systems, known as linear complementarity, systems. it is well-known that checking certain controllability properties of very simple piecewise linear systems are undecidable problems. In an earlier paper, however, a complete characterization of the controllability of the so-called conewise linear systems has been achieved. By employing this characterization and exploiting the special structure of linear complementarity systems, we present a set of inequality-type conditions as necessary and sufficient conditions for their controllability. Our treatment is based on the ideas and the techniques from geometric control theory together with mathematical programming.