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This paper investigates the problem of robust H ∞ repetitive control for a class of linear stochastic switched systems with time delay. Based on the lifting technique, a continuous-discrete stochastic 2D (two-dimensional) delayed model is firstly proposed to describe the control and learning actions of the repetitive control system. Then a sufficient condition for the asymptotical stability with H ∞ performance of the 2D model is derived by choosing an appropriate common Lyapunov functional. The feedback controller gains are then obtained by solving a set of linear matrix inequalities. One example is given to illustrate the effectiveness of the proposed method.

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This paper concerns the design of an observer-based repetitive control system (RCS) to improve the periodic disturbance rejection performance. The periodic disturbance is estimated by a repetitive learning based estimator (RLE) and rejected by incorporation of the estimation into a repetitive control (RC) input. Firstly, the configuration of the observer-based RCS with the RLE is described. Then, a continuous–discrete two-dimensional (2D) model is built to describe the RCS. By choosing an appropriate Lyapunov functional, a sufficient condition is proposed to guarantee the stability of the RCS. Finally, a numerical example is given to verify the effectiveness of the proposed method.

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