The main contribution is to present stability analysis criterion for a type of norm⁃bounded uncertain perturbed discrete systems(NUPDS) with its states is subjected to a novel ellipsoidal outer approximation,which is different from the traditional bound description of general state. Based on the Lyapunov method, a delay dependent criterion and the corresponding state feedback control law, which are expressed in terms of linear matrix inequalities(LMIs) technology, are proposed to guarantee the asymptotic stability for the perturb delay systems. The solution of the LMIs can be obtained easily using existing efficient convex optimization techniques. A numerical example is given to illustrate effectiveness of the proposed method.