Parametrization and reliable extraction of proper compensators

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 gives a system whose poles are specified by Dk. The subclass is navigated and extracted through a conventional parametrization whose denominators are affine to row echelon form and the centre is in a compensator whose numerator has minimum column degrees. Applications include stabilization of linear multivariable systems.