Robust Schur polynomial stability and Kharitonov´s theorem

The paper considers robust stability properties for Schur polynomials of the form f(z) = ??i=0 nan-izi By plotting coefficient variations in planes defined by variable pairs ai, an-i for each i and requiring in each such plane the region of obtained coefficients to be bounded by lines of slope 45??, 90?? and 135??, we show that stability for all polynomials defined by comer points is necessary and sufficient for stability of all polynomials defined by any points in the region. Using this idea, one can construct several necessity and differing sufficiency conditions for the stability of polynomials where each ai can vary independently in an interval [ai, a- i]. As the sufficiency conditions become closer to necessity conditions the number of distinct polynomials for which stability has to be tested increases.