We review the polynomial matrix compensator equation XlDr + YlNr = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (Nr,Dr) is given by the strictly proper rational plant right matrix-fraction P = NrD−1 r , (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and… (More)

The polynomial matrix equation X\Dr + Y\Nr = Dk is solved for those X\ and Y\ that give proper transfer functions X^~Y\ characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly proper transfer function NrDr l such that wrapping the negative unity feedback round the cascade… (More)

The aim of this work is to develop parallel concepts of column reduced polynomial matrices for proper rational matrices. A definition of column reducedness for a class of proper rational matrices is proposed and the properties of such matrices are studied, in particular reduction to column reduced form by elementary operations over the ring of proper… (More)