A matrix pencil approach to the Morgan's problem

The problem of decoupling a nonsquare state space system by state feedback with singular input transformation is considered. The problem is solved by conducting a finite search for decouplable square systems, appropriately derived from the original. Decoupling feedback on any of these systems defines the decoupling feedback for the original. The issue of fixed poles is also considered and the possibility of selecting the uncontrollable poles is investigated.