Realization and partial fractions

AbstractWe discuss the relation between two intrinsically different proposals that have been made in the literature concerning the representation by constant matrices of rational matrices given in fractional form. It turns out that the relation is most naturally studied in the framework of partial-fraction decompositions. We develop the realization theory for decompositions with respect to arbitrary complementary parts of the extended complex plane which may, for instance, correspond to stability and instability. An isomorphism is obtained which connects the spaces used in the two methods, and several identities relating to the McMillan degree are derived in a direct way. Finally, a new computational procedure is given to obtain the partial-fraction decomposition of a rational matrix given in fractional form