Some robust stability theorems for polygons of discrete polynomials

How to partition an unstable polytope of polynomials into stable and unstable regions is addressed. L.R. Pujara and N. Shanghag have taken the first step by proposing a partition algorithm for unstable polygons of continuous polynomials. The present study begins with a discrete version of the segment lemma of H. Chapellat and S.P. Battacharyya (1989). Some necessary and sufficient conditions are proven for a polynomial vanishing at e* (where *=J omega /sub 0/), for some omega /sub 0/, in a polygon of discrete polynomials. These results lead directly to a method for partitioning polygons of discrete polynomials.<>