Sampled-data repetitive control for a class of non-minimum phase nonlinear systems subject to period variation

The robust sampled-data repetitive control (RC, or repetitive controller, also designated RC) problem for non-minimum phase nonlinear systems is both challenging and practical. This paper proposes a sampled-data output-feedback RC design for a class of non-minimum phase systems with measurable nonlinearities to improve the robustness against the period variation. The design relies on additive-state decomposition, by which the output-feedback RC problem is decomposed into an output-feedback RC problem for a linear time-invariant component and a state-feedback stabilisation problem for a nonlinear component. Thanks to the decomposition, existing controller design methods in both the frequency domain and the time domain are employed to make the robustness and discretisation for a continuous-time nonlinear system tractable. In order to demonstrate the effectiveness, an illustrative example is given.