Self-bounded controlled invariant subspaces in measurable signal decoupling with stability: minimal-order feedforward solution for non-left-invertible systems

The structural properties of self-bounded controlled invariant subspaces are fundamental to the synthesis of a dynamic feedforward compensator achieving insensitivity of the controlled output to a disturbance input accessible for measurement, on the assumption that the system is stable or pre-stabilized by an inner feedback. The control system herein devised has several important features: i) minimum order of the feedforward compensator; ii) minimum number of unassignable dynamics internal to the feedforward compensator; iii) maximum number of dynamics, external to the feedforward compensator, arbitrarily assignable by a possible inner feedback. From the numerical point of view, the design method herein detailed does not involve any computation of eigenspaces, which may be critical for systems of high order. The procedure is first presented for left-invertible systems. Then, it is extended to non-left-invertible systems by means of a simple, strictly geometric, squaring-down technique.