Abstract: The edge check results of the continuous interval systems are first extended to the interval discrete systems by employing the convex analysis way of value set. Further, in order to obtain some vertex check results, the discussion is limited to such a case when only lower-order coefficients of transfer function of the discrete system are disturbed. It is shown that the closed-loop stability of an interval discrete system with a first-order controller can be guaranteed by that of its vertex plants provide that the pole of the controller satisfies the corresponding inequality conditions on the highest order of the disturbed coefficients. Here, the argument growing principle plays an important role in the proof of the main conclusion. An example is also included for illustrating the obtained results.