Disturbance decoupling problems via dynamic output feedback

This paper considers the disturbance decoupling problems, with or without internal stability and pole placement, via dynamic output feedback using polynomial and rational matrix techniques. We show that in all three problems considered, the central solvability condition can be expressed as a two-sided matching problemA = BXC, whereA, B, andCare the polynomial system matrices of certain natural subsystems of the system model andXis to be determined over various subrings of the rational functions. This matching problem can in turn be reduced to certain appropriate zero-cancellation conditions on the polynomial system matricesA, B, andC.