A new approach is presented in the study of the linear-quadratic control problem of singularly perturbed discrete systems with a prescribed degree of stability. All the poles of the resulting closed-loop system are constrained to lie in a circle with the radius of 1/α. By applying a bilinear transformation, near-optimum controller design is presented in terms of continuous reduced-order problems. The stiffness problem due to the singularly perturbed system is eliminated. The method is very suitable for parallel programming. A numerical example demonstrates the efficiency of the proposed method.