Distance problems for linear dynamical systems

Abstract

This chapter is concerned with distance problems for linear timeinvariant differential and differential-algebraic equations. Such problems can be formulated as distance problems for matrices and pencils. In the first part, we discuss characterizations of the distance of a regular matrix pencil to the set of singular matrix pencils. The second part focuses on the distance of a stablematrix or pencil to the set of unstable matrices or pencils.We present a survey of numerical procedures to compute or estimate these distances by taking into account some of the historical developments as well as the state of the art.