 
Summary: WA4 10:15
ON THE COMMON (LEFT,RIGHT) DIVISORS OF TWO POLYNOMIAL MATRICES
P.J. Antsaklis
Department of Electrical Engineering
University of Notre Dame
Notre Dame, IN 46556
Summary
The notions of common right and common left
divisors of two polynomial matricesare well es
tablished. They can be used to characterize the
unobservable and the uncontrollable modesof a sys
tem and to study polynomialmatrix equations of the
form alVl + a V = V3. The new notion of common
(right,left) divisorsof two polynomial matrices
is introduced here and it is used tocharacterize
the modesof the systemwhich are both uncontrol
lable and unobservable; it is also used to study
polynomial matrix equationsof the form
where N(qxp) , D(rxm)andV(qxm) are given poly
nomial matrices; (1) has attracted recently consid
