  Robustness is a basic property of any control system. In the context of
linear output regulation, it was proved that embedding an internal model of the
exogenous signals is necessary and sufficient to achieve tracking of the
desired reference signals in spite of external disturbances and parametric
uncertainties. This result is commonly known as "internal model principle". A
complete extension of such linear result to general nonlinear systems is still
an open problem, which is exacerbated by the large number of alternative
definitions of uncertainty and desired control goals that are possible in a
nonlinear setting. In this paper, we develop a general framework in which all
these different notions can be formally characterized in a unifying way.
Classical results are reinterpreted in the proposed setting, and new results
and insights are presented with a focus on robust rejection/tracking of
arbitrary harmonic content. Moreover, we show by counter-example that, in the
relevant case of continuous unstructured uncertainties, there are problems for
which no smooth finite-dimensional robust regulator exists ensuring exact
regulation.
