Robust schur polynomial stability and kharitonovs theorem

The paper considers robust stability properties for Schur polynomials of the form <inline-formula> <inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href="tcon_a_8906089_o_ilm0001.gif"/> </inline-formula>. By plotting coefficient variations in planes defined by variablei-o pairs a,-, an.{ 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 corner 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 a_I can vary independently in an interval [<underline>a </underline>sub>i, ā]. As the sufficiency conditions become closer to necessity conditions the number of distinct polynomials for which stability has to be tested increases.