Divisors of polynomial matrices: Theory and applications

In this note divisors
G(s)
of a given polynomial matrix
N(s)
are discussed. The note deals with the following problems: extraction of a greatest right (left) divisor of
N(s)
, computation for a given state-space system
(C, A, B)
a state-space feedback making the system
(C, A + BF, B)
maximally or appropriately observable, and determination for a given system
(C, A, B, O, W, O)
a disturbance rejection feedback
F
. The developed methods are very simple from a computational point of view and can be easily implemented in the software via existing computer library procedures.