Characterization of polynomials whose stability domain convex hull is a polyhedron

The authors investigate some geometrical properties of the domain of (generalized) stability in the coefficient space for a monic n th-order polynomial. Regions of root location such that the convex hull of the corresponding domain of stability 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. These results are exploited in the design of filters solving the robust strict positive realness problem for families of rational functions with uncertainty in the numerator