A 2D-based approach to guaranteed cost repetitive control for uncertain discrete-time systems

This paper presents a two-dimensional (2D)-based approach to the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The objective is to design a control law such that the closed-loop repetitive control system is robustly stable and a certain bound of performance criteria is guaranteed for all admissible uncertainties. It is shown first how the proposed repetitive control scheme can be equivalently formulated in the form of a distinct class of 2D system. Then, sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI), and the control law matrices are characterized by the feasible solutions to this LMI. Moreover, an optimization problem is introduced to efficiently solve the optimal guaranteed cost control law by minimizing the upper bound of the cost function. The proposed approach is applicable not only to SISO systems, but also to MIMO systems. Two numerical examples are provided to demonstrate the effectiveness of the proposed controller design procedures.