Robust predictive control for uncertain singularly perturbed systems

In this paper, In this paper, a robust predictive control problem for a class of uncertain singularly perturbed systems is studied. By using state feedback control, the specific design steps and methods of the new robust predictive controller are given. Firstly, based on linear matrix inequality method, Lyapunov stability theory, the optimization problem under linear quadratic performance index is solved online, and the constraints of the controller and a set of piecewise continuous state feedback control sequences are obtained. It is further proved that there is the feasible solution of the optimization problem at the initial time. On this basis, it is guaranteed that the uncertain singularly perturbed system is regular, stable, impulse free. Finally, the correctness and effectiveness of the method are verified by a simulation example.