Robust Schur stability of a polytope of polynomials

The main objective of the authors is to provide a necessary and sufficient condition for a polytope of polynomials to have all its zeros inside the unit circle. The criterion obtained serves as a discrete-time counterpart for results in S. Bialas (1985) and F. Fu and B.R. Barmish (1987) for the continuous case. Also, the results are reduced to operations on (n-1)×(n-1) matrices. It is concluded that, by the edge result of A.C. Bartlett et al. (1987), it suffices to check the exposed edges in order to determine whether a polytope of polynomials has all its zeros in a simply connected region D