Distance to the nearest uncontrollable pair and algebraic Riccati equation

Abstract

A connection is established between nearness to unstabilizability of a stabilizable pair (A, B) of matrices, and nearness to singularity of the symmetric positive definite solution to an associated algebraic Riccati equation. From this result, computable upper and lower bounds are derived for the distance of (A, B) to the nearest uncontrollable pair.<>