A robust guaranteed cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, the repetitive controller combined with preview compensator is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed cost preview repetitive control problem is transformed into the guaranteed cost control problem for the augmented dynamic system. For given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) techniques. By incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included to show the effectiveness of the proposed method.
In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.
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