Based on Lyapunov stability theory and linear matrix inequalities (LMIs) method, parameter-dependent and parameter- independent states feedback controller, the states feedback controller and dynamic output feedback controller are designed, respectively. The necessary and sufficient condition of existence the above controllers are given by LMIs. Considering the disturbance and noise, the mixed robust H2 / H8 performance of the discretetime polytopic uncertain system is proposed, which is used to improve the system transient performance and to ensure the robustness of the system simultaneously. Finally, the robust states feedback and dynamic output feedback controllers are designed and an example is given to show its effectiveness. [ABSTRACT FROM AUTHOR]