On determining the δ and &thetas; Hurwitz stability of interval polynomials

Develops two results that can be used for estimating the root space boundary of an interval polynomial family without using the excessive computations associated with the edge theorem. The particular root space boundary to be estimated consists of a straight line parallel to the imaginary axis and two other straight lines of finite, non-zero slope passing through the origin. The notions of δ Hurwitz and θ Hurwitz stability are introduced and it is shown that to ascertain the δ or θ Hurwitz stability of an interval polynomial family, it is sufficient to check that the vertices of that family have the same property. A similar vertex result is also derived for an interval-plant fixed-controller pair under the assumption that the controller is of a special form. The results here constitute a useful tool for classical control design under parametric uncertainty