A note on regulation of nonlinear non minimum-phase systems with unknown high-frequency gain

In this note we extend the design tool presented in out previous works for robust stabilization of nonminimum-phase nonlinear systems to the case of output regulation problems. Se take advantage from a design tool known in the linear literature as ``vibrational feedback'' to handle the presence of unstable zero dynamics in output regulation problems in presence of uncertainties. This work frames in a research attempt of the authors to fully characterize, in terms of necessary and sufficient conditions, the problem of nonlinear output regulation for nonminimum-phase systems in presence of strong uncertainties. In this respect, the emphasis of the contribution is to provide a sufficient condition under which the problem at hand can be solved in presence of strong uncertainties on the high-frequency gain.