STRICTLY DOUBLY COPRIME FACTORIZATIONS AND ALL STABILIZING COMPENSATORS RELATED TO REDUCED-ORDER OBSERVERS

Doubly coprime factorizations (DCF) play an important role in the desi gn of compensators for lumped linear time invariant systems. They are defined as stable proper rational matrices, and they not only constitu te a starting point for the fractional approach to all stabilizing com pensators, but they are also closely related to the frequency domain d esign of (optimal) state feedback and estimation, and of the resulting observer-based compensators. When defining DCFs related to reduced-or der observers, some rational matrices become improper. This can be pre vented by the introduction of artificial (stable) dynamics-the identit y elements-which cancel in the system and in the compensator transfer matrices. Such pole-zero cancellations, however, are contrary to the u sual notion of coprimeness. It is shown here that these additional dyn amics, which have no meaning in an observer-based compensator scheme a re superfluous, and that the parametrization of all stabilizing compen sators is feasible on the basis of possibly nonproper factorizations n ot containing identity elements. For such factorizations, the new defi nition of strictly doubly coprime factorizations (SDCF) is proposed.