REMARKS ON ORTHOGONAL POLYNOMIALS AND BALANCED REALIZATIONS

Given a proper antistable rational transfer function g, a balanced rea lization of g is constructed as a matrix representation of the abstrac t shift realization introduced by Fuhrmann (1976). The required basis is constructed as a union of sets of polynomials orthogonal with respe ct to weights given by the squares of the absolute values of minimal d egree Schmidt vectors of the corresponding Hankel operators. This exte nds results of Fuhrmann (1991), obtained in the generic case.