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

Abstract

For the investigation of the robust stability of control systems with structured uncertainties many results have been presented recently that lead to stability tests of the edges of a polytope. In this paper some results are discussed where the stability of an edge is guaranteed by the stability of the vertices of the edge. Given the characteristic polynomial of a closed loop system with structured uncertainties in the parameters; for special types of uncertainties the family of polynomials is defined by a polytope in the space of parameters. In the frequency domain the corresponding value set of the family, for s = jw fixed, is a polygon whose edges are formed by the so-called exposed edges of the polytope. For the investigation of the stability of the polynomial family these exposed edges must be tested (Kraus and Truol 1991 a). This test can be simplified if an edge has the vertex property, i.e. if the stability of the edge is guaranteed by the stability of the two vertices.