State Feedback Guaranteed Cost Repetitive Control for Uncertain Discrete‐Time Systems

Abstract

This paper considers the problem of guaranteed cost repetitive control for uncertain discrete‐time systems. The uncertainty in the system is assumed to be norm‐bounded and time‐varying. The objective is to develop a novel design method so that the closed‐loop repetitive control system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. The state feedback control technique is used in the paper. While for the case that the states are not measurable, an observer‐based control scheme is adopted. Sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI). The control and observer gains are characterized by the feasible solutions to these LMIs. The optimal guaranteed cost control law is obtained efficiently by solving an optimization problem with LMI constraints using existing convex optimization algorithms. A simulation example is provided to illustrate the validity of the proposed method.