For the discrete stochastic system of the uncertainty with a class of bounded norm, the guaranteed cost control
with the output feedback controller is studied, and the general form of the quadratic performance index upper bound for the closed-loop system is achieved. By using LMI convex optimal technique, the approach of designing the optimal guaranteed cost controller which makes the closed-loop system asymptotically stable is derived. Finally, the simulation example shows the feasibility and effectiveness of the presented method.