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.