A theorem is established to study the robust stability of a set of specified rectangle polynomials. It is shown that, for the defined super rectangle, the stability of all of the vertex polynomials for a discrete-time system can ensure the stability of all of the polynomials inside the rectangle. This is a counterpart of Kharitonov's theorem (weak version) for discrete-time systems. For interval polynomials, a sufficient condition is presented to check the stability of the whole set of polynomials, which has shown to be better than that given in N. K. Bose and E. Zeheb (1988).
