this paper, a robust H. model predictive control (MPC) technique is proposed for time-varying uncertain discrete-time systems in the presence of input constraints and disturbances. We formulate a minimization problem of the upper bound of finite horizon cost function subject to the terminal inequality for an induced l(2)-norm bound. In order to improve system performance, we propose an LMI condition for the terminal inequality by using relaxation matrices. The LMI condition guarantees induced l(2)-norm bounds of the system despite system uncertainty and disturbance. A numerical example shows the effectiveness of the proposed method.