Geometric methods for invariant-zero cancellation in linear multivariable systems with application to signal rejection with preview

This work deals with zero cancellation in linear multivariable systems with possible feedthrough terms from the inputs to the outputs. A methodology for the synthesis of a minimal-order feedforward compensator preserving key properties of the original system while cancelling minimum-phase invariant zeros is derived by means of the basic tools of the geometric approach. The properties maintained in the feedforward compensation scheme are stabilizability and right-invertibility. Duality arguments show how to modify the devised method so as to achieve zero cancellation with a cascade filter retaining detectability and left-invertibility. Continuous and discrete-time systems are considered in a unified framework exploiting the common structural features. An original application of zero cancellation to signal rejection with preview is presented. A novel feedforward control scheme is devised, avoiding the steering along minimum-phase zero techniques that are at the basis of well-settled solutions.