Minimality, stabilizability, and strong stabilizability of uncertain plants

This paper considers a set of uncertain transfer functions whose numerator and denominators belong to independent polytopes. It shows that i) the members of this set are free from pole-zero cancellations iff 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, ii) the members of this set are free from pole zero cancellations in the closed right half plane, iff 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 iii) in the strictly proper case, all plants in the set are strongly stabilizable iff all plants avoid pole-zero cancellations in the closed right half plane and all the corner ratios are strongly stabilizable. A counter-example is presented to show that this last result does not extend to biproper plants