AN ANALYSIS OF THE POLE PLACEMENT PROBLEM. I. THE SINGLE-INPUT CASE
Volker Mehrmann, Hongguo Xu · 1996
For the solution of the single-input pole placement problem we derive explicit ex- pressions for the feedback gain matrix as well as the eigenvector matrix of the closed-loop system. Based on these formulas we study the conditioning of the pole-placement problem in terms of per- turbations in the data and show how the conditioning depends on the condition number of the closed loop eigenvector matrix, which is a similar to a generalized Cauchy matrix, the norm of the feedback vector and the distance to uncontrollability.