Stability conditions for polytopes of polynomials

The stability of linear systems with uncertain parameters is addressed. The author treats the mathematical problem of deciding whether or not all polynomials in some specified family are Ω-stable (have all their zeros in the subset Ω of the complex plane). For a general stability region in the complex plane, a stability criterion for polytopes of polynomials is given in terms of the stability of a minimal number of corners and edges of the polytope. The ´testing set´ of edges and corners depends entirely on the edge directions of the polytope, hence the results are particularly applicable when the directions are fixed, but the lengths and positions of the edges are allowed to vary. Applications to robust pole placement of uncertain systems and computation of worst case H∞ norms are demonstrated