Model reduction problem of linear discrete systems: Admissibles initial states

Abstract

Given a linear discrete system with initial state x0 and output function yi , we investigate a low dimensional linear system that produces, with a tolerance index ǫ , the same output function when the initial state belongs to a specified set, called ǫ-admissible set, that we characterize by a finite number of inequalities. We also give an algorithm which allows us to determine an ǫ-admissible set.