An LMI approach to robust model predictive sampled-data control for linear uncertain systems

In this paper, we consider digital receding horizon control for a continuous-time plant by a sampled-data approach. We first present a piecewise constant robust model predictive control for uncertain linear systems. Then, using an uncertain linear system as a design model, we introduce feedback tuning to robust model predictive control to compensate model mismatch and disturbances. The solution procedures proposed in this paper are formulated as optimization problems subject to linear matrix inequalities. The conditions for closed-loop stability of the sampled-data control system when the proposed receding horizon control procedures are employed are also established. Finally, we present a numerical example to demonstrate the effectiveness of the control procedures.