Stability conditions for polytopes of polynomials

In considering the stability or performance of linear systems with uncertain parameters one is led to consider the simultaneous stability of families of polynomials. For a general stability region in the complex plane, the author gives a stability criterion for polytopes of polynomials 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 to problems with fixed directions, but varying lengths and positions of the edges. Applications to robust pole placement of uncertain systems and computation of worst case H_∞ norms are demonstrated