Convexity properties of polynomials with assigned root location

This paper presents some geometrical results on the domain of (generalized) stability for a family of nth order polynomials. Regions of root location such that the convex hull of the corresponding domain of stability in the coefficient space is a polyhedron are investigated, and specific regions for which the convex hull is an n+1 vertex polyhedron are derived. The discrete-time stability domain falls in the latter class of regions. Implications of the results for the design of filters solving the robust strict positive realness for families of rational transfer functions with uncertainty in the numerator are also developed.