An angle metric through the notion of Grassmann representative

Abstract

The present paper has two main goals. Firstly, to introduce different metric topologies on the pencils (F,G) associated with autonomous singular (or regular) linear differential or difference systems. Secondly, to establish a new angle metric which is described by decomposable multi-vectors called Grassmann representatives (or Pl¨ucker coordinates) of the corresponding subspaces. A unified framework is provided by connecting the new results to known ones, thus aiding in the deeper understanding of various structural aspects of matrix pencils in system theory.