Differential representations of multivariable linear systems with disturbances and polynomial matrix equationsPX + RY = WandPX + YN = V

A unified state-space approach to polynomial matrix equations
PX + R Y = W, PX + YN = V
based on a generalization of the Wolovich-Guidorzi formula has been presented. In this paper a connection is shown between the solutions of the above equations and differential representations for multivariable linear systems with disturbances. Applications are presented for stable synthesis of certain types of compensators.