Geometric methods for invariant zero cancellation in discrete-time non-strictly-proper linear multivariable systems

This paper presents a geometric procedure for designing a minimal-order dynamic feedforward compensator whose aim is cancelling the minimum-phase invariant zeros of a discrete-time linear multivariable system, non-strictly proper in general. The feedforward compensator also satisfies the condition of being of minimal dynamic order and that of maintaining right invertibility: i.e., if the original system is right invertible, then the cascade of the feedforward compensator and the system is right invertible as well. Special attention is paid to this property since it is a basic property in interesting control problems, like, e.g., reference tracking. Nonetheless, the procedure is developed for non-right-invertible and non-left- invertible systems, in general.