On unbounded directions of linear interval parametric systems and their extensions to AE solutions

Abstract

We consider a system of linear equations, whose coefficients depend linearly on interval parameters. Its solution set is defined as the set of all solutions of all admissible realizations of the parameters. We study unbounded directions of the solution set and its relation with its kernel. The kernel of a matrix characterizes unbounded direction in the real case and in the case of ordinary interval systems. In the general parametric case, however, this is not completely true. There is still a close relation preserved, which we discuss in the paper. Nevertheless, we identify several special sub-classes, for which the characterization remains valid. Next, we extend the results to the so called AE parametric systems, which are defined by forall-exists quantification.