Abstract

Fig. 2 shows the disturbance signals. Finally, the reference signal is shown in Fig. 3 (upper plot). The linear matrix inequality of Theorem 2 is feasible in this case and The lower plot in Fig. 3 confirms that the overall design task is achieved and the next stage would be to attempt to tune the design. V. CONCLUSIONS The major contributions in this short paper are i) the application of lifting techniques to transform the bi-directional dynamics into those of an equivalent uni-directional repetitive process model and hence the availability of a stability theory and control law design to achieve this basic property, and ii) the first results on stability plus performance in the case when there are disturbances present, which are assumed to be periodic over twice the pass length. Also there is clearly much work to do before these results can be evaluated on physical examples. This includes a wide range of algorithms for control law design, robustness