Robust H_∞ model predictive control for uncertain systems using relaxation matrices

In 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 l2-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 l2-norm bounds of the system despite system uncertainty and disturbance. A numerical example shows the effectiveness of the proposed method.