Minimality, stabilizability and strong stabilizability of uncertain plants

The authors consider a set of uncertain transfer functions whose numerators and denominators belong to independent polytopes. It is shown: (1) that the members of this set are free from pole-zero cancellations if all the ratios of numerator edges and denominator edges are free from pole-zero cancellations and the numerator and denominator corners evaluated at a finite number of points satisfy certain phase conditions; (2) that the members of this set are free from pole-zero cancellations in the closed right half plane, if all the ratios of numerator edges and denominator edges are free from pole-zero cancellations in the closed right half plane, and the numerator and denominator corners evaluated at a finite number of points satisfy certain phase conditions; and (3) that in the strictly proper case, all plants in the set are strongly stabilizable if all plants avoid pole-zero cancellations in the closed right half plane and all the corner ratios are strongly stabilizable. A counterexample is presented to show that this last result does not extend to biproper plants