Test of convex directions for robust stability

We address the stability problem of a segment of polynomials. The polynomial which defines the direction of the segment is called a convex direction if the stability of the whole segment is implied by that of its extreme members, regardless where the segment lies. Such a property plays an important role in robust stability analysis, and a necessary and sufficient condition, called phase growth condition, has been given by Rantzer (1992). In this paper, we provide alternative necessary and sufficient conditions which will allow us to determine in a finite number of rational operations if a given polynomial is a convex direction