On pole placement via eigenstructure assignment approach

This note comes back to the hard problem of pole placement by static output feedback: let a triplet of matrices {A; B; C} be given with n state variables, m inputs and p ouputs, find a matrix K such that the spectrum of A + B K C equals a specified set. When mp > m + p, a simple noniterative technique based upon the notion of eigenstructure that, in most cases, assigns m + p roots is proposed. It, therefore, enables the designer to assign the whole of the desired spectrum when m + p = n mp. Index Terms--Eigenstructure, Kimura's condition, pole placement.