LMI based robust output feedback MPC

This paper presents the synthesis of a robust model predictive controller (MPC) derived from an input-output representation with uncertainty. According to MPC approach, at each sampling time, the controller is calculated by minimizing an upper bound of a quadratic cost function over infinite time horizon. The optimization problem and the associated constraints on the input and output process are formulated in terms of linear matrix inequalities (LMI). From the input-output representation, an extended state space model is constructed, where the state is composed of present and past values of the system\´s inputs and outputs. The control is obtained as a function of known output and input signals, hence there is no need for any estimate of the unmeasured states, as it would be necessary in the "traditional" state space modelization. The proposed algorithm is illustrated on numerical examples.