  The discrete-time robust repetitive control (RC, or repetitive controller,
also designated RC) problem for nonlinear systems is both challenging and
practical. This paper proposes a discrete-time output-feedback RC design for a
class of systems subject to measurable nonlinearities to track reference
robustly with respect to 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 system and a
state-feedback stabilization problem for a nonlinear system. Thanks to the
decomposition, existing controller design methods in both the frequency domain
and time domain can be employed to make the robustness and discretization for a
nonlinear system tractable. To demonstrate the effectiveness, an illustrative
example is given.
