On the decoupling of linear systems using proportional and derivative state feedback

The problem considered is that of finding, for a linear time invariant system x˙(t)=Ax(t)+Bu(t), y(t)=Cx(t), a PD state feedback u(t)=F_dx˙(t)+F_px(t)+r(t) such that y(t)=r(t). Also, geometric conditions which guarantee the existence of such a solution are to be found. Existing methods are briefly discussed, then the authors give an alternative solution in terms of operators without using the Brunovsky canonical form. They assume right-invertibility, which is necessary for row-by-row decoupling