Robust control via convex approximation of the stability region

A Schur invariant transformation on the coefficient space of polynomials is used to obtain a sufficient stability condition in terms of simplexes. The order of polynomials could be increased step by step starting from some low order stable simplex. A stability measure is introduced as a minimal distance between the extreme points of interval system and the surface of the stable simplex. A straightforward robust controller design procedure is proposed for interval plants. Some low order examples are given.