Robust stability of control systems: extreme point results for the stability of edges

In the investigation of the robust stability of control systems with structured uncertainties, many results have been presented that lead to stability tests of the edges of a polytope. Some results are discussed where the stability of an edge can be guaranteed by the stability of the vertices of the edge. For two types of stability-the Schur and a rational D-stability-the conditions for the vertex property of an edge are obtained from the decomposition of the edge polynomials. The associated polynomial families, which can result by control of uncertain plants, are discussed