Study of robust stability for discrete-time systems

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)