Robust predictive control for a class of uncertain discrete system with multiple state delays

A robust predictive control algorithm based on memory state feedback is proposed for a class of uncertain discrete time system with input constraint and multiple state delays. By introducing Lyapunov-Krasovskii function and using linear matrix inequality (LMI) method, the algorithm can convert the infinite time domain optimization problems into linear programming problems. Sufficient conditions of the existence and explicit expression for the memory state feedback controller are obtained, and the control input can satisfy constraint as well. Asymptotical stability of the closed-loop system and minimum of robust performance index can be guaranteed simultaneously. Finally, the simulation results illustrate the effectiveness of the proposed algorithm.